Subject: NA Digest, V. 94, # 48 NA Digest Monday, November 28, 1994 Volume 94 : Issue 48 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: Flaw in Pentium Chip The Pentium Division Bug German Scientific Computing Home Page FTP Reports from SAM at ETH Zuerich MATLAB Code for Integer Programming Call for IVP Test Set Problems Software for Semidefinite Programming Modified Godunov Methods NA Summer School -- 1995: 2nd Announcement Seminar on Numerical Methods for PDE in Italy Conference on Numerical Mathematics Honoring Mike Powell Institue for Mathematics and its Applications Winter Tutorials Mathematics of Neural Networks SPIE Ill-posed Inverse Problems Symposium Conference on Flow through Porous Media Positions at City Polytechnic of Hong Kong Positions at Simon Fraser Centre Positions at the Australian National University Position at BEAM in Ithaca, NY New Book on Numerical Methods for Shallow-water Flow Contents, Transactions on Mathematical Software Springer Verlag Journals Preview Service Contents: Interval Computations; Contents, BIT Submissions for NA Digest: Mail to na.digest@na-net.ornl.gov. Information about NA-NET: Mail to na.help@na-net.ornl.gov. ------------------------------------------------------- From: Gene Golub Date: Thu, 24 Nov 94 11:44:09 PST Subject: Flaw in Pentium Chip In NY Times for Nov. 24, there is an article by John Markoff describing an error in division operation of the Pentium chip made by INTEL. (The article is on the business pages which seems to be where most computer announcements are made!) There are quotes by Velvel Kahan and Cleve Moler (there is also a photo of Cleve). I think it is good to call such problems to the attention of our colleagues and students. It would be good if we could help the manufacturers in debugging their chips before they are released. Thank goodness we have the efforts of Kahan but we need a more concerted effort. Gene ------------------------------ From: Cleve Moler Date: Mon Nov 28 22:13:20 EST 1994 Subject: The Pentium Division Bug Hi, all -- I've been unusually busy the last week. I would like to write something specially for the NA Digest that explains why, but I'm afraid I don't have enough time tonight. Maybe I can do something by next week. In the meantime, you might go browsing through the following. -- Cleve Pentium Papers Repository The MathWorks is making a collection of "primary source" material on the Pentium division bug available. If you're wired to the Web, try www.mathworks.com -- "What's New" button or, with anonymous FTP, try ftp.mathworks.com -- directory /pub/tech-support/moler/Pentium The documents available as of today, 11/28/94, are listed below. This archive is intended as a reasonably complete historical record of the events associated with the Pentium floating point division bug. All of these documents are reproduced as they originally appeared on the Net or elsewhere with full credit given to the authors and institutions involved. Some material may be copyrighted and should be treated as such. Nicely_original_post.txt October 30. Memo from Prof. Thomas Nicely, Lynchburg College. Calculations involving prime numbers lead to the first description of the bug. Example is 1/824633702441. Mathisen_first_post.txt October 30. A series of Internet postings by Terje Mathisen, Norsk Hydro, Norway, confirming the bug and lead to a test program, p87test.zip. EE_Times.txt November 7. Article by Alex Wolfe in the EE Times, a weekly trade publication with the headline, INTEL FIXES A PENTIUM FPU GLITCH Copyright (c) 1994 by the EE Times Coe.txt November 15. Internet posting by Tim Coe, Vitesse Semiconductor, with a model of the chip's behavior and the example 4195835/3145727. Moler_first_post.txt November 15. Internet posting by Cleve Moler, the MathWorks, summarizing results to date. Examples include Nicely's prime reciprocal and Coe's ratio. Cable_News_Network.txt November 22. Report by Steve Young on CNN's Moneyline includes interviews with Intel's Stephen Smith and Moler. MathWorks_press_release.txt November 23. MathWorks issues a press release with the title THE MATHWORKS DEVELOPS FIX FOR THE INTEL PENTIUM(tm) FLOATING POINT ERROR New_York_Times.txt November 24. New York Times article by John Markoff with headline CIRCUIT FLAW CAUSES PENTIUM CHIP TO MISCALCULATE, INTEL ADMITS Copyright (c) 1994 by the New York Times Associated_Press.txt November 24. News story circulated by the Associated Press. Copyright (c) 1994 by the Associated Press Moler_second_post.txt November 24. Internet posting by Moler describing a software/ hardware workaround for the FDIV bug. Moler_third_post.txt November 24. Internet posting by Moler announcing a Pentium-Aware Release of MATLAB. Intel_support.txt November 24. America OnLine and Internet posting by Ken Hendren, Intel Applications Support Manager. Intel_FAX.txt Intel FAXBACK Document #7999 Obtained from FAXBACK system at 800 628-2283 Nicely_second_post.txt November 25. Memo from Prof. Nicely entitled "Pentium Bug and the Intel NDA". Andy_Grove.txt November 27. Internet posting by Intel CEO Andy Grove entitled "My Perspective on Pentium". ------------------------------ From: Ulrich Ruede Date: Mon, 21 Nov 1994 19:30:11 +0100 Subject: German Scientific Computing Home Page German Scientific Computing Home Page We have recently started to provide a collection of WWW pages accessible via URL http://www5.informatik.tu-muenchen.de/sci-comp/home.html These documents collect information about Scientific Computing in Germany. We invite the active participation of the Scientifc Computing Community both within Germany and internationally. All feedback to scicomp@informatik.tu-muenchen.de is welcome. Please help to make this service useful by sending us the information you have! Uli Ruede Ulrich Ruede Institut fuer Informatik, Technische Universitaet, D-80290 Muenchen, Germany, e-mail: ruede@informatik.tu-muenchen.de Tel: +49 89 21058238, Fax: +49 89 21052022 URL: http://www5.informatik.tu-muenchen.de/persons/ruede.html ------------------------------ From: bpohl@sam.math.ethz.ch Date: Tue, 22 Nov 94 18:51:47 +0100 Subject: FTP Reports from SAM at ETH Zuerich The Seminar fuer Angewandte Mathematik (SAM) at ETH Zuerich now has an anonymous ftp-site from which you can ftp the research reports, published at SAM. To get there type ftp ftp.sam.math.ethz.ch Then login as anonymous, give your e-mail address as a password, then cd pub/sam-reports You can get the file README and follow the instructions given in that file. If you have difficulties, questions or suggestions please contact Nicholas D. Ironmonger SAM ETH Zuerich CH-8092 Zuerich Tel: ++41 - 1 632 23 57 FAX: ++41 - 1 632 10 85 e-mail: ndi@sam.math.ethz.ch ------------------------------ From: Plamen Yalamov Date: Thu, 24 Nov 1994 12:53:09 +0200 Subject: MATLAB Code for Integer Programming Dear NA-NETers, Is anyone aware of a MATLAB code for INTEGER PROGRAMMING ? I have the Optimization Toolbox but there is nothing in this toolbox. Could anyone send such a piece to me if it is free? Plamen Yalamov ------------------------------ From: Walter Lioen Date: Mon, 28 Nov 1994 15:59:01 GMT Subject: Call for IVP Test Set Problems We, the Initial Value Problem group of Peter van der Houwen of the numerical mathematics department of CWI, Amsterdam are working on parallel ODE/DAE solvers in a project called `Parallel Codes for Circuit Analysis and Control Engineering'. At present we have parallel codes for ODEs and we are at the point of adding the DAE part. However, for both categories of problems we have a lack of good (i.e., large and difficult) test problems. Presently Alfredo Bellen at Triest is composing a test set. This set will be our point of departure, but we want to extend this test set. If we succeed in this effort, both a descriptive report, and problem sources, will be made available by anonymous ftp. We are interested in: - real life problems, for example but not limited to electrical circuits, chemical reactions, control engineering; - preferably published in the open literature; - stiff (at least, on parts of the integration interval); - high dimension (100-1000 or even larger); - for the DAEs, the index should be restricted to 2; - because of the desired dimension some machine readable format preferably Fortran source but C, Pascal and Maple are also welcome; - all you can tell us about the solution; - permission to make it publically available (of course with the proper acknowledgements). If you can not fulfil all of our wishes, but got the point, please do not hesitate to react. The project's group members are: Peter J. van der Houwen project leader, Walter Hoffmann second project leader, Ben P. Sommeijer senior researcher, Jacques J.B. de Swart PhD. student, Wolter van der Veen PhD. student, Walter M. Lioen scientific programmer. Walter Hoffmann is of the University of Amsterdam. All other members are working at CWI. Please send a small description of what you could offer (and how you score on our overcharged wish list) to one of: bsom@cwi.nl, jacques@cwi.nl, wolter@cwi.nl. Thanks in advance, Walter M. Lioen CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. e-mail: walter@cwi.nl phone: +31 20 5924101 fax: +31 20 5924199 telex: 12571 mactr nl ------------------------------ From: Lieven Vandenberghe Date: Fri, 25 Nov 1994 09:26:15 +0100 Subject: Software for Semidefinite Programming Semidefinite Programming Software and Survey Paper available In semidefinite programming we minimize a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite. Semidefinite programming unifies several standard problems (e.g., linear and quadratic programming) and finds many applications in control, structural optimization, combinatorial optimization, and other fields. Although semidefinite programs are much more general than linear programs, they can be solved as efficiently. Most interior-point methods for linear programming have been generalized to semidefinite programs. As in linear programming, these methods have polynomial worst-case complexity, and perform very well in practice. A software package and a survey paper are now available via anonymous ftp. The software consists of C-source that calls LAPACK and also some matlab routines that work with a mex-file interface. To get the software, ftp as anonymous to isl.stanford.edu, and cd to pub/boyd/semidef_prog. Set binary mode and get the file semidef_prog.tar.Z (which includes semidef_prog.ps.Z, the corresponding survey paper), and the appropriate mex-file. Quit ftp. Uncompress and untar semidef_prog.tar.Z: your-machine> zcat semidef.tar.Z | tar xvf - You will then have a directory semidef which contains source code, postscript documentation, source for matlab mex interfaces, and example matlab files. You can get the survey paper alone in pub/boyd/reports, in the file semidef_prog.ps.Z. You may also be interested in several related papers available via anonymous ftp in pub/boyd/reports, e.g., pri_dual.ps.Z, mit-talk.ps.Z, ifac_eng_des.ps.Z. Lieven Vandenberghe (K.U. Leuven) Stephen Boyd (Stanford University) ------------------------------ From: M. Abouziarov Date: Fri, 25 Nov 1994 14:08 -0600 Subject: Modified Godunov Methods Dear frends. I have read your e-mail address in internet system and decided to write you such letter: I am mathematician from Russia, my name is Moustafa Abouziarov. I have graduated from Moscow Physical-Technical Institute in 1981, received doctor's degree in 1990, now I work in Mexico. I am a specialist in numerical methods of continuum mechanics, especially in Godunov's method , and the major result of my scientific work is the modification of this well-known difference The advantages of my modification of Godunov's method are: 1. the second order accuracy in space and time is achieved for the case of two and three 3-D variables, one must account also for the variations due to the transversal gradients; 2. no increase of the adjacent cell number is required for analyzing the cell; 3. there is no difference between Euler case and Lagrang one. 4. the second order is achieved on the irregular and moving meshes,where Godunov's method does not provide even the first-order accuracy; 5. introduction of the first-order scheme predictor step after the analysis of the spline for pressure makes it possible to avoid non-physical oscillations; 6. the second-order approximation on the "rigid wall"- type boundary is achieved; 7. no substantional modifications of the present software systems ,based on Godunov's method, are required; 8. the controlled viscosity makes it possible to handle the Navier-Stokes equations,using the scheme for the Euler equations; 9. the approach is easily extended to the versions of Godu- nov's method for simulating the elastic-plastic flows and handling the Timoshenko-type shell equations. 10. the present modifications is essentially effective to analyze 3-D problems of high-energy shocks in fluids and gases and the hypersonic flows. I used this modification of Godunov's method to analyze 2-D problems of high-energy shocks,generated by detonation of solid explosive, in fluids and gases in elastic-plastic tanks. I received reliable results. Then I have extended my modification for nonlinear case. In this case it is necessary to take into account some nonlinear properties of Riemann's problem solution and the quadratic spline for density. My results are similar or better than [1]. But I have some problem, I think you know it. If I solve the test from [1] about interaction of two blast wave as a two-dimensional problem ( X is direction of propagation of waves) with the rigged walls on Y=Y0 and on Y=Y1 (conservative boundary conditions on Y direction) on Y direction I receive some oscillations of pressure and density and I receive Y direction velocity. The altitude of this oscillations may be about 10% or more for pressure. Somebody calls it as nonlinear nonstability. I do not know how to avoid this nonphysical oscillations. They are generated by rigged body boundary conditions. So I would like to have contact with specialists in this area to solve this and some other problems, conserning modifications of Godunov's method for some other kinds of equations, lenearized Navier-Stokes equations for example, different state equations and etc. If you know e-mails addresses of such specialists ( [1] and etc.) in USA and etc., please, send me them. [1] Colella P. and Woodword P. The Piecewise Parabolic method for Gas-Dynamical Simulations. // J. Comp. Phys. 1984. V. 54. P. 174 - 202. My e-mail address: < abouziarov@iievms1.iiecuer.unam.mx > Best regards M.Abouziarov. ------------------------------ From: Gene Golub Date: Sun, 20 Nov 94 17:49:07 PST Subject: NA Summer School -- 1995: 2nd Announcement AMS-SIAM Summer Seminar in Applied Mathematics "Mathematics of Numerical Analysis: Real Number Algorithms" Park City, Utah, July 17--August 11, 1995 The twenty-fifth AMS--SIAM Summer Seminar in Applied Mathematics will be held July 17--August 11, 1995 at the Prospector Square Inn and Conference Center, Park City, Utah. The seminar will be sponsored by the American Mathematical Society, the Society for Industrial and Applied Mathematics, and the International Mathematical Union. It is anticipated that the seminar will be partially supported by grants from federal agencies. The proceedings will be published by the AMS in the "Lectures in Applied Mathematics" series. The mathematical theory of real number algorithms is to be the subject of this proposed conference. Thus numerical analysis will be central with emphasis on geometrical, algebraic, analytic, and foundational perspectives. Investigations of efficiency will play a special role. Practical algorithms will be the subject of theoretical analysis, but immediate useful results will not be demanded. It is hoped that the conference will give the subject of numerical analysis a greater coherence through a focus on the mathematical side. In particular, to aim to strengthen the unity of mathematics and numerical analysis, and to narrow the gap between pure and applied mathematics. That goal is appropriate since many of the heroes of pure and applied mathematics, Newton, Euler, Lagrange, and Gauss among them, established the basic real number algorithms. With the revolution of the computer and the great achievements of scientific computation, it does service to both the pure and applied communities to support the mathematical development of numerical analysis. This is an appropriate time to schedule such a meeting in view of the rapid development of heuristic work, a good base of theoretical work, and a widespread desire for mathematical deepening of the subject. The conference will be international in character with strong representation from the most mathematically developed parts of numerical analysis. Besides tutorials and short courses, seminars in the following areas are contemplated: linear algebra, nonlinear systems-path following, differential equations, linear programming problems, algebraic questions, foundations, information based complexity, lower bounds, and approximation theory. The organizing committee includes Eugene L. Allgower, Colorado State University; Lenore Blum, MSRI; Alexandre J. Chorin, University of California, Berkeley; Philippe G. Ciarlet, Universit\'e Pierre et Marie Curie, Paris; Felipe Cucker, Universitat Pampeu Fabra, Spain; James W. Demmel, University of California, Berkeley; Ronald A. DeVore, University of South Carolina, Columbia; Gene H. Golub, Stanford University; Arieh Iserles, University of Cambridge, UK; Hubertus Th. Jongen, Reinisch-Westf Tech Hochschule, Aachen, Germany; Herb Keller, California Institute of Technology; Jacques Louis Lions, College de France; James M. Renegar, Cornell University; Steve Smale (Chair), University of California, Berkeley; Michael Shub, IBM; Gilbert Strang, MIT; Shmuel Winograd, IBM; and Henryk Wozniakowski, University of Warsaw and Columbia University. To date the following have accepted invitations to speak: All members of the organizing committee; Roger Brockett, Harvard University; John Canny, University of California, Berkeley; W. Dahmen, Reinisch-Westf Tech Hochschule, Aachen, Germany; David Donoho, University of California, Berkeley; James G. Glimm, SUNY at Stony Brook; N. Karmarker, A T & T Bell Laboratories; T. Y. Li, Michigan State University; Arkadi Nemirovski, Israel Institute of Technology; Victor Pan, Herbert H. Lehman College, CUNY; Vladimir Rokhlin, Yale University; Marie-Francoise Roy, Universit\'e de Rennes; Roger Temam, Indiana University; Richard S. Varga, Kent State University; Victor A. V. Vassiliev, Institute for System Studies, Moscow; Margaret H. Wright, A T & T Bell Laboratories; Yosef Yomdin, Weizmann Institute of Science, Israel; Mike Powell, Cambridge; and D. Grigoriev, Penn State (Tentative). Park City is a popular summer vacation destination with a comfortable, temperate climate in the mountains of Utah. Housing for participants has been arranged at the Prospector Square Inn and Conference Center. Inexpensive restaurants, food shops, and other attractions are within walking distance of the Inn. The Prospector Square Inn includes eight buildings with rustic ski lodge style accommodations, in addition to a large lecture hall and meeting rooms. A sports center including pool, exercise machines, racquetball courts, etc. (all available for an extra charge) is located on the property. All rooms being held for participants contain two double- or queen-sized beds, television, telephone, microwave oven, and refrigerator. Some units have full kitchens. The daily cost is $45 single or double occupancy ($50 triple and $55 quad) plus 10.25% lodging tax. Note that these prices are per room, not per person. For those attending the full four weeks of the seminar, a very limited number of one-, two-, and three-bedroom condominium units is available on a monthly basis. Those interested should contact the conference coordinator. More detailed information, including how to make reservations, will be included with the official invitation to the seminar. There is a registration fee of $40. Everyone interested receiving an invitation to attend should send the following information before February 15, 1995, to AMS--Summer Seminar Conference Coordinator, AMS Meetings and Conferences Department, P.O. Box 6887, Providence, RI 02940; e-mail dls@math.ams.org. Please type or print the following: 1. Full name and mailing address; 2. Telephone number and area code for office and home; 3. E-mail address if available; 4. Anticipated arrival and departure dates; 5. Your scientific background relevant to the topic of the seminar; please indicate if you are a student or if you received your Ph.D. on or after 7/1/89; 6. Financial assistance requested (please estimate cost of travel); indicate if support is not required and if interested in attending even if support is not offered. 7. Indicate if you would like to be included on a list of those desiring a roommate for the seminar. If yes, please indicate if you are male or female, and list any other pertinent information (i.e., smoking/nonsmoking). Special encouragement is extended to junior scientists to apply. A special pool of funds expected from federal agencies has been earmarked for this group. Other participants who wish to apply for a grant-in-aid should so indicate; however, funds available for the seminar are very limited, and individuals who can obtain support from other sources should do so. Advanced graduate students are encouraged to participate. ------------------------------ From: Claudio Canuto Date: Mon, 21 Nov 1994 15:20:42 GMT+1 Subject: Seminar on Numerical Methods for PDE in Italy POLITECNICO DI TORINO ISTITUTO DI ANALISI NUMERICA DEL C.N.R. Dipartimento di Matematica Pavia Seminar on RECENT ADVANCES IN NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS Politecnico di Torino - February 14-16, 1995 TOPICS: adaptivity and a-posteriori error estimates, multi-level techniques (hierarchical bases, wavelets, non-linear Galerkin methods), discretization methods for multi-scale phenomena. INVITED LECTURERS: R.E.BANK (San Diego) W.DAHMEN (Aachen) S.JAFFARD (E.N.P.C.) C.JOHNSON (Goteborg) Y.MADAY (Paris VI) A.T.PATERA (M.I.T.) R.TEMAM (Orsay) R.VERFUERTH (Bochum) J.XU (PennState) H.YSERENTANT (Tubingen) CALL FOR CONTRIBUTIONS: in addition to the invited seminars, a limited number of short contributions on the themes of the Seminar will be presented. People interested should submit a title and a one-page abstract to one of the Organizers BEFORE JANUARY 15, 1995 at the addresses below. REGISTRATION FEE: a registration fee of 180,000 Italian Lire (reduced to 150,000 It.Lire for members of SIMAI or affiliated organizations, and to 100,000 It.Lire for students) will be required to cover lunches, coffee-breaks and social activities. ACCOMMODATION: Hotel accommodation in Torino will be available at special discount rates (from 80,000 It.Lire in a **-hotel to 150,000 It.Lire in a ****-hotel, per single room per day, continental breakfast included). INFORMATION AND REGISTRATION: People interested in the Seminar should contact one of the Organizers at the addresses below BEFORE JANUARY 15, 1995, preferably using fax or e-mail. ORGANIZATION: The Seminar is organized with the collaboration of SIMAI, ASI, Cassa di Risparmio di Torino, and other funding institutions. CLAUDIO CANUTO ALESSANDRO RUSSO Dipartimento di Matematica Istituto di Analisi Numerica Politecnico di Torino Consiglio Nazionale delle Ricerche corso Duca degli Abruzzi, 24 via Abbiategrasso, 209 I-10129 Torino ITALY I-27100 Pavia ITALY tel. +39 11 564 7543 tel. +39 382 529 600 fax +39 11 564 7599 fax +39 382 529 566 e-mail: ccanuto@polito.it e-mail: russo@dragon.ian.pv.cnr.it ------------------------------ From: Arieh Iserles Date: Mon, 21 Nov 94 22:05:42 GMT Subject: Conference on Numerical Mathematics Honoring Mike Powell Conference on Numerical Mathematics Celebrating the 60th Birthday of M.J.D. Powell University of Cambridge, England 27--30 July 1996 The opportunity for this conference is provided by the sixtieth birthday of one of the world's leading numerical mathematicians, whose contributions to optimization and approximation have been decisive. The real purpose, however, is to celebrate numerical mathematics and scientific computing. The University of Cambridge, where Mike Powell has been for the last eighteen years the John Humphrey Plummer Professor of Applied Numerical Analysis, is a suitable setting for this event. The participants will be accommodated at historic Magdalene College, in the city centre of Cambridge. There will be ten invited, longer lectures that focus on optimization and approximation theory, but submitted papers, addressing themselves to original and timely research, are welcome in all fields of numerical mathematics. We would now like to call for papers to be presented at this conference. All such papers will be considered for inclusion into a proceedings. They can be submitted to either Martin Buhmann or Arieh Iserles, by e-mail or otherwise. Every submission should contain the title of the talk and an abstract. The duration of submitted talks will be 25 minutes. The invited speakers are Ian Barrodale (Victoria, B.C.) Carl de Boor (University of Wisconsin at Madison) Roger Fletcher (University of Dundee) Gene Golub (Stanford University) Charles Micchelli (IBM Yorktown Heights) Jorge More (Argonne National Laboratory) Beresford Parlett (University of California at Berkeley) Mike Powell (University of Cambridge) Mike Todd (Cornell University) Philippe Toint (University of Namur) The organizing committee consists of Ian Barrodale (Victoria, B.C.), Martin Buhmann (ETH Zurich), Wolfgang Dahmen (RWTH Aachen), Roger Fletcher (University of Dundee), Arieh Iserles (University of Cambridge), Will Light (University of Leicester), Bill Morton (University of Oxford), Mike Todd (Cornell University) and Philippe Toint (University of Namur). Support for the conference is provided by the London Mathematical Society. For more information contact: * M.D. Buhmann Mathematik Departement ETH Zentrum 8092 Zurich Switzerland E-Mail: mdb@math.ethz.ch or * A. Iserles Department of Applied Mathematics and Theoretical Physics Silver Street Cambridge CB3 9EW England E-Mail: ai@amtp.cam.ac.uk ------------------------------ From: Robert Gulliver Date: Wed, 23 Nov 94 12:50:40 CST Received: by s2.ima.umn.edu; Wed, 23 Nov 94 12:50:40 CST Subject: Institue for Mathematics and its Applications Winter Tutorials During Winter, 1995 the Institute for Mathematics and its Applications in Minneapolis will hold two tutorials on Inverse Problems in Wave Propagation. The January 17-20 tutorial will emphasise electromagnetic waves, with applications to tomography and random media; survey talks by David Colton, Adel Faridani, and George Papanicolaou are planned. The January 30-February 3 tutorial will be more closely relevant to acoustic waves, e.g. as applied in acoustic microscopy (geophysics) and seismology; the IMA expects to hear talks from Jan Achenbach, Christof Stork, William Symes and Gunther Uhlmann. For more information contact ima-staff@ima.umn.edu. ------------------------------ From: J. C. Mason Organization: The University of Huddersfield HEC Subject: Mathematics of Neural Networks CALL FOR PAPERS - MATHEMATICS of NEURAL NETWORKS and APPLICATIONS (MANNA 1995) International Conference at Lady Margaret Hall, Oxford, July 3-7, 1995 - run by the Universities of Huddersfield and Brighton - with support from the London Mathematical Society We are delighted to announce the first conference on the Mathematics of Neural Networks and Applications (MANNA), in which we aim to provide both top class research and a friendly motivating atmosphere. Applications of neural networks (NNs) have often been carried out with a limited understanding of the underlying mathematics but it is now essential that fuller account should be taken of the many topics that contribute to NNs: approximation theory, control theory, genetic algorithms, dynamical systems, numerical analysis, optimisation, statistical decision theory, statistical mechanics, computability and information theory, etc. . We aim to consider the links between these topics and the insights they offer, and identify mathematical tools and techniques for analysing and developing NN theories, algorithms and applications. Working sessions and panel discussions are planned. Keynote speakers who have provisionally accepted invitations include: N M Allinson (York University, UK) S Grossberg (Boston, USA) S-i Amari (Tokyo) M Hirsch (Berkeley, USA) N Biggs (LSE, London) T Poggio (MIT, USA) G Cybenko (Dartmouth USA) H Ritter (Bielefeld,Germany) J G Taylor (King's College, London) P C Parks (Oxford) It is anticipated that up to 40 contributed papers will be presented. The proceedings will be published, probably as a volume of an international journal, and contributed papers will be considered for inclusion. The deadline for submission of abstracts is 17 February 1995. Accommodation will be available at Lady Margaret Hall (LMH) where many rooms have en-suite facilities. The conference will start with Monday lunch and end with Friday lunch, and there will be a full-board charge (including conference dinner) of about 235 pounds for this period as well as a conference fee of 195 pounds. We expect to be able to offer a reduction in fee to those who give submitted papers, and a very low fee to a number of recommended bona-fide students who book early. There will be a supporting social programme, including reception, outing(s) and conference dinner, and family accommodation may be arranged in local guest houses. Committee: S W Ellacott (Brighton) and J C Mason (Huddersfield) (Organisers) ; I Aleksander, N M Allinson, N Biggs, C M Bishop, D Lowe, P C Parks, J G Taylor, K Warwick For information, contact: Mrs R.Hawkins, School of Computing and Mathematics, University of Huddersfield, Queensgate , Huddersfield HD1 3DH Email: R.Hawkins@hud.ac.uk Phone: 44+(0)484 472150 ------------------------------ From: Chris Johnson Date: Thu, 24 Nov 1994 14:06:15 -0700 Subject: SPIE Ill-posed Inverse Problems Symposium Call for Papers Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications Conference Chairs: Randall L. Barbour, SUNY/Brooklyn; Mark J. Carvlin, Bristol-Myers Squibb Co.; Michael A. Fiddy, Univ. of Massachusetts/Lowell Program Committee: David Isaacson, Rensselaer Polytechnic Institute; Norman J. McCormick, Univ. of Washington; Michael V. Klibanov, Univ. of North Carolina/Charlotte; Christopher R. Johnson, Univ. of Utah; Robert V. McGahan, Rome Lab. Part of SPIE's 1995 International Symposium July 9-14, 1995 San Diego Convention Center San Diego, CA Imaging methods are increasingly being applied to a wide range of applications that include clinical medicine, geophysics, remote sensing, and materials testing. Sources can be magnetic, acoustic, electrical, or electromagnetic in origin. These may be located external to the medium or inside. Detection modes may or may not be time dependent and can range from backscatter only to full tomographic measurement schemes. A common feature complicating many of these methods is the uncertainty regarding the volume of medium probed by the penetrating or emitted energy. Frequently, this uncertainty is due to the effects of scattering. Accurate knowledge of the energy distribution requires information about the medium, which is the unknown being examined. As a result, useful methods frequently must consider approximate solutions that represent compromises between computational effort, physical accuracy of the modeling scheme, and quality and type of available data. Principal topics of interest will fall into three main areas: (1) mathematical aspects of inverse methods (e.g., dealing with ill-conditioning, limited noisy data, missing phase information, superresolution, etc.); (2) modeling methods for forward and inverse scattering phenomena (e.g., approximate solutions to integral equations of scattering, finite difference time domain, and projection tomographic techniques); and (3) interdisciplinary applications, including clinical medicine, optics, astronomy, remote sensing, etc. This conference will bring together leading experts from universities, medical centers, government laboratories, and industry to discuss the latest developments in the diverse and fast developing field. Chris Johnson, Ph.D. Department of Computer Science University of Utah Email: crj@cs.utah.edu WWW: http://www.cs.utah.edu/~crj ------------------------------ From: Claude Carasso Date: Mon, 28 Nov 94 16:07:49 +0100 Subject: Conference on Flow through Porous Media INTERNATIONAL CONFERENCE ON MATHEMATICAL MODELLING OF FLOW THROUGH POROUS MEDIA MAY 22-26, 1995 SAINT-ETIENNE (FRANCE) ORGANIZING COMMITTEE A. BOURGEAT, C. CARASSO (France), R. EWING (USA), S. LUCKHAUS (Allemagne), A. MIKELIC (France), M. PRIMICERIO (Italie) FIRST LIST OF PARTICIPANTS I. AGANOVIC (Croatie), G. ALLAIRE (France), S. ANTONTSEV (Espagne), M. AVELLANEDA (U.S.A.), C.I. BARENBLATT (Russie), J. BEAR (Israel), G. CHAVENT (France), J.H. CUSHMAN (U.S.A.), G. DAGAN (Israel), J. DOUGLAS Jr (U.S.A.), H. ENE (Roumanie), A.FASANO (Italie), T. GALLOUET (France), I.W. GELHAR (U.S.A.), R. GILBERT (U.S.A.), J. GLIMM (U.S.A.), R.A. GREENKORN (U.S.A.), A. GUTJAHR (U.S.A.), U. HORNUNG (Allemagne), S. KOZLOV (France), R. LENORMAND (France) V.N. MONAKHOV (Russie), G.PANASENKO (France), P.PANFILOV (Russie), G.PAPANICOLAOU (U.S.A.), M.QUINTARD (France), T.F RUSSEL (U.S.A.), J.M.THOMAS (France), C.J.VAN DUIJN (Hollande), M.F. WHEELER (U.S.A.), S.WHITAKER (U.S.A.), Y.C. YORTSOS (U.S.A.), V.ZHIKOV (Russie) AIM OF THE CONFERENCE The main goal of this conference is to bring together leading researchers in the field of modelling flow in porous media and to provide a forum for discussion on thecurrent state of modelling. The conference will address both the pure theoretical question in modelling and the use of various models in numerical simulations. The conference areas of interest focus on : - Pore scale models, macropores, fractured media, percolation - Scaling up, averaging, macrodispersion and homogenization - Filtration of non Newtonian fluids, multiphase flow and contaminant transport - Free and moving boundary problems - Geochemical models, reactive porous media - Numerical simulation of flows and transport phenomena in porous media SCIENTIFIC PROGRAM AND PUBLICATION In addition to the invited lectures a number of posters sessions will take place. The conference proceedings will be published and will mainly include the lectures and selected posters. Moreover there will be a poster session devoted to industrial research activities REGISTRATIONFEE Before April 1st / after April 1st Delegate from a company 2 500 FF 2 900 FF University Members 1 200 FF 1 500 FF INFORMATIONS Congres Milieux Poreux, Analyse Numerique, 23 rue du Dr Paul Michelon 42023 Saint Etienne cedex 2. FRANCE Tel. : (33) 77.42.15.35-Fax. : (33) 77.25.60.71 e-mail : cmp@anumsun1.univ-st-etienne.fr For more details please connect by e-mail to : cmpinfo@anumsun1.univ-st-etienne.fr or with mosaic, gopher or xgopher at : gopher://gopher.univ-st-etienne.fr. ------------------------------ From: Daniel Ho Date: Mon, 21 Nov 1994 10:56:10 +0800 Subject: Positions at City Polytechnic of Hong Kong City Polytechnic of Hong Kong (City University of Hong Kong - designate) The City Polytechnic of Hong Kong is a well established degree- granting institution in Hong Kong funded by the government through the University and Polytechnic Grants Committee. Its current student population is 15,158 and the number is expected to grow to 16,000 by the mid-1990's. The Polytechnic is committed to excellence in teaching and research and to a close relationship with the community and industry. The medium of instruction is English. Applications are invited for the following posts: University Lectures Department of Mathematics [Ref.A/164/43] The Department is seeking applicants for two positions to begin in September 1995. One position is for a Numerical analyst specialized in numerical solution of partial differential equations and the other position can be in any field of Applied Mathematics. Applicants should have a PhD in Mathematics or a related discipline with strong research record or excellent research potential as well as a commitment to teaching undergraduate and postgraduate students. Salary: HK$34,415 - $57,490 per month (Exchange rate: US$1 = HK$7.8 approximately) Appointment may be on superannuable terms with provision for retirement benefit or on a fixed term contract with gratuity payable at 15% of basic salary upon completion of contract. Generous fringe benefits include medical and dental schemes, long leave and housing assistance where applicable. Further information can be obtained from the Personnel Office, City Polytechnic of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong (Fax: 852-7881154/852-7889334, E-mail: PORECRUT@CITYU.EDU.HK) or from Professor Roderick S.C. Wong, Head of Department of Mathematics (E-mail: MAWONG@CITYU.EDU.HK). Please apply with a curriculum vitae including a list of publications, a statement describing current and planned research, and the names and addresses of three academic referees to the Personnel Office by the end of February 1995. ------------------------------ From: Loki Jorgenson Date: Sun, 20 Nov 1994 23:44:52 -0800 (PST) Subject: Positions at Simon Fraser Centre SIMON FRASER CENTRE FOR EXPERIMENTAL AND CONSTRUCTIVE MATHEMATICS (For more information on the Centre's activities, see the CECM prospectus available through the CECM Information Services at gopher.cecm.sfu.ca or http://www.cecm.sfu.ca) The Centre is soliciting applications for one or two POST-DOCTORAL FELLOWS and/or RESEARCH ASSOCIATES commencing after July 1, 1995, in any areas compatible with the interests of the centre (specifically aspects of computationally assisted mathematical analysis, number theory and discrete mathematics). Applicants with a PhD in Mathematics, Computer Science or Operations Research will be favoured. The PDFs are primarily research positions though some teaching may be involved. Research associates may be involved in significant software development. Applicants should send a curriculum vitae and arrange for three letters of reference to be sent to Dr. J.M. Borwein, Director CECM, Department of Mathematics and Statistics, Simon Fraser University, Burnaby B.C., V5A 1S6. Applicants should list relevant work and educational experience; interested candidates should look at the at the Centre's prospectus for more information (see above). For RESEARCH ASSOCIATES a strong background in computing is preferred with a knowledge of FORTRAN, LISP, C or C++ (as well as OOP) considered an asset although not essential. A familiarity with mathematical problem-solving platforms (such as MATLAB, Maple, Mathematica, Macsyma, MuPAD, Pari, etc.), either as a user or as a programmer, is also helpful. This Centre located in Burnaby, British Columbia (Greater Vancouver) is dedicated to further research and graduate education in Computation in the Mathematical Sciences. The Centre provides a sophisticated mix of computation, experimentation and mathematics. Of interest are questions on how one uses the computer: To build intuition? To generate hypotheses? To validate conjectures or prove theorems? To discover nontrivial examples and counter-examples? The steering committee consists of J. Borwein (Director), P. Borwein, L. Goddyn, L. Jorgenson, R. Russell, and M. Trummer. Inquiries may be directed to J. Borwein at the CECM or via Email to jborwein@cecm.sfu.ca. ------------------------------ From: Markus Hegland Date: Wed, 23 Nov 1994 12:45:03 +1100 Subject: Positions at the Australian National University THE AUSTRALIAN NATIONAL UNIVERSITY SCHOOL OF MATHEMATICAL SCIENCES CENTRE FOR MATHEMATICS AND ITS APPLICATIONS POSTDOCTORAL FELLOW/RESEARCH FELLOW ( LEVEL A/LEVEL B) IN ADVANCED COMPUTATION Applications are invited for appointment to a position at the level of Postdoctoral Fellow or Research Fellow in the Advanced Computation and Modelling Program of the Centre for Mathematics & its Applications. The current research interests of the program includes mathematical software research and development, numerical methods for partial differential equations optimization including applications to statistical computing, and inverse problems. Appointments will be made for periods of up to three years and may be extended. The initial level of appointment, depending on the candidate's experience and qualifications, will lie within the following salary ranges: Postdoctoral Fellow [Level A] $36,795-$39,495 p.a. Research Fellow [Level B] $41,574-$49,370 p.a. Assistance with relocation expenses may also be provided. Part-time appointment may be available as well as an extended visiting appointment during a period of leave of absence from a home institution. Enquires and requests for further information including selection criteria can be addressed to Professor M R Osborne (email Mike.Osborne@maths.anu.edu.au Fax 06 2490759). Professor Osborne can be contacted at Texas A&M University until December 16 1994 (email mike@cs.tamu.edu). Closing Date: 23 January 1994 Ref: SMS 15.11.1 Email addresses and/or fax numbers should be provided for referees so that appointment procedures can be expedited. APPLICATIONS addressing the selection criteria should be submitted in duplicate to The Secretary, The Australian National University, Canberra, ACT 0200 quoting reference number and including curriculum vitae, list of publications and names and addresses of at least three referees. Further information is available from either of the contacts listed above. The University has a "no smoking" policy effective in all University buildings and vehicles. ------------------------------ From: Gal Berkooz Date: Tue, 22 Nov 1994 22:41:19 -0500 Subject: Position at BEAM in Ithaca, NY BEAM Engineering and Applied Research 205 W. Court St. Ithaca, New York 14850 Employment Opportunity Research & Development Scientist / CFD-Flow Optimization Status: Full time exempt position. Supervision received: Reports to President/Project Leader. Supervision exercised: Scientific programmers/None. Date posted: 11/16/1994. Start Date: 2/1/1995 or when qualified applicant is selected. Location: Ithaca, NY. Job Summary: Develop and modify production CFD codes with turbulence models to perform flow analysis and flow optimization. Work to integrate CFD-Flow Optimization software into other software products. Participate in the development of flow analysis and other scientific software. Participate in solving and analyzing specific configurations related to jet flows and complex geometry nozzles. Write technical reports and present results to government and industry concerns. Competency Required: Ability to develop high quality numerical codes. Ability to integrate developed code with other existing software. Ability to independently initiate and pursue technical objectives. Excellent communications and team-working skills. Education/Experience Required: A Ph.D. in fluids mechanics or applied mathematics involving the development and application of flow optimization codes or equivalent work experience. At least two years of post-doctoral work or equivalent experience required. Applications from promising recent graduates will be considered. Experience in industry a plus. Experience with numerical analysis, and analyzing and choosing algorithms. Some experience with generating geometries for complex configurations. Experience with development of GUIUs a plus. Salary and Benefits: Salary of $45,000-$65,000 commensurate with qualifications and experience. BEAM offers a comprehensive benefits package and stock ownership programs. Ithaca offers a low cost of living and a high quality of life. Send resume to: President BEAM Engineering and Applied Research c/o Search 102 205 W. Court St. Ithaca NY 14850 ------------------------------ From: C.B. Vreugdenhil Date: Wed, 23 Nov 1994 09:51:35 +0100 Subject: New Book on Numerical Methods for Shallow-water Flow New book. Numerical methods for shallow-water flow by C.B. Vreugdenhil Kluwer Academic Publishers, Dordrecht 1994 ISBN 0-7923-3164-8 261 pages Price Dfl 185 Shallow-water problems occur in a wide variety, such as atmospheric flows, tides, storm surges, river and coastal flows, lake flows, tsunamis. Numerical simulation is an effective tool to solve them and a great variety of numerical methods are available. The first part of the book summarizes the basic physics of shallow-water flow needed to use numerical methods in various conditions. The second part gives an overview of possible numerical methods, not only with their stability and accuracy properties but also with an assessment of performance in various conditions. This enables the reader to make a choice for particular applications. Correct treatment of boundary conditions (often neglected) is emphasized. The greater part of the book is about two-dimensional shallow-water equations but a discussion of the 3-d form is included. The book is intended for researchers and users of shallow-water models in oceanographic and meteorological institutes, hydraulic engineering and consulting. It also provides a major source of information to applied and numerical mathematicians. Contents: 1. Shallow-water flows 2. Equations 3. Some properties 4. Behaviour of solutions 5. Boundary conditions 6. Discretization in space 7. Effects of space discretization on wave propagation 8. Time integration methods 9. Effect of time integration on wave propagation 10. Numerical treatment of boundary conditions 11. Three-dimensional shallow-water flow C.B.Vreugdenhil Institute for Marine and Atmospheric Research Utrecht (IMAU) Princetonplein 5 3584 CC Utrecht The Netherlands phone +31 30 533167 fax +31 30 543163 email vreugdhl@fys.ruu.nl ------------------------------ From: Ron Boisvert Date: Mon, 21 Nov 94 17:32:04 EST Subject: Contents, Transactions on Mathematical Software (Note : Information on TOMS, including complete searchable Table of Contents of all volumes and upcoming papers, is available on the World Wide Web at http://gams.nist.gov/toms/.) Table of Contents ACM Transactions on Mathematical Software (TOMS) Volume 20, Number 3 (September 1994) Patrick F. Cummins and Geoffrey K. Vallis, Algorithm 732: Solvers for Self-Adjoint Elliptic Problems in Irregular Two-Dimensional Domains, pp. 247-261. Dieter Kraft, Algorithm 733: TOMP -- Fortran Modules for Optimal Control Calculations, pp. 262-281. Victoria Z. Averbukh and Samuel Figueroa and Tamar Schlick, Remark on Algorithm 566, pp. 282-285. Jorge More and David J. Thuente, Line Search Algorithms With Guaranteed Sufficient Decrease, pp. 286-307. A. G. Buckley, Conversion to Fortran 90: A Case Study, pp. 308-353. A. G. Buckley, Algorithm 734: A Fortran 90 Code for Unconstrained Nonlinear Minimization, pp. 354-372. K. Kim and J.L. Nazareth, A Primal Null-space Affine Scaling Method, pp. 373-392. Barry W. Brown and Lawrence Levy, Certification of Algorithm 708: Significant Digit Computation of the Incomplete Beta, pp. 393-397. Carl Taswell and Kevin C. McGill, Algorithm 735: Wavelet Transform Algorithms for Finite Duration Discrete-Time Signals, pp. 398-412. ------------------------------ From: SVJPS@vax.ntp.springer.de Date: Tue, 22 Nov 1994 21:26:06 +0000 (N) Subject: Springer Verlag Journals Preview Service CC Springer Journals Preview Service via Internet CC CC --------------------------------------------------------------------- CC Numerische Mathematik ISSN 0029-599X CC Volume 69 Number 1 (1994) code 211 file T4069001.211 CC --------------------------------------------------------------------- CC CC Editor-in-Chief: CC P.G. Ciarlet, Paris CC R.S. Varga, Kent CC CC Managing Editor: CC C. Zenger, Muenchen CC CC CC Aims and Scope: CC Numerische Mathematik publishes papers of the very highest quality CC presenting significantly new and important developments in all areas CC of Numerical Analysis. Numerical Analysis is here understood in its CC most general sense, as that part of Mathematics that covers: CC 1. The conception and mathematical analysis of efficient numerical CC schemes actually used on computers (the core of Numerical Analysis) CC 2. Optimization and Control Theory CC 3. Mathematical Modeling CC 4. The mathematical aspects of Scientific Computing CC CC Subscription information: CC Volumes 66-68 (4 issues each) will appear in 1994. CC CC Copyright: Springer-Verlag Berlin Heidelberg 1994 CC CC ===================================================================== CC Numerische Mathematik ISSN 0029-599X CC CONTENTS Volume 69 Number 1 (1994) CC --------------------------------------------------------------------- CC AU Axelsson-O. Chronopoulos-A-T. TI On nonlinear generalized conjugate gradient methods. SO Numer.-Math.. 1994 69(1) P 1. AB 40690001.211 AU Elsner-L. He-C. Mehrmann-V. TI Minimizing the condition number of a positive definite matrix by completion. SO Numer.-Math.. 1994 69(1) P 17. AB 40690017.211 AU Engl-H-W. Grever-W. TI Using the L--curve for determining optimal regularization parameters. SO Numer.-Math.. 1994 69(1) P 25. AB 40690025.211 AU Laval-G. Mas-Gallic-S. Raviart-P-A. TI Paraxial approximation of ultrarelativistic intense beams. SO Numer.-Math.. 1994 69(1) P 33. AB 40690033.211 AU Marek-I. Szyld-D-B. TI Local convergence of the (exact and inexact) iterative aggregation method for linear systems and Markov operators. SO Numer.-Math.. 1994 69(1) P 61. AB 40690061.211 AU Schmidt-G. TI Boundary element discretization of Poincar\'e--Steklov operators. SO Numer.-Math.. 1994 69(1) P 83. AB 40690083.211 AU Spann-W. TI Error estimates for the approximation of semicoercive variational inequalities. SO Numer.-Math.. 1994 69(1) P 103. AB 40690103.211 AU Zerner-M. TI An asymptotically optimal finite element scheme for the arch problem. SO Numer.-Math.. 1994 69(1) P 117. 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CC CC Information is based on the cited source documents. The accuracy of CC these documents cannot be guaranteed. Springer-Verlag makes no CC warranty, either express or implied, with respect to the use of any CC information and assumes no liabilities for loss or damage, whether CC such loss or damage is caused by error or omission. CC CC Tables of contents and BiblioAbstracts are provided for information CC purposes only. If you discover an error, please contact us. CC CC Copyright for Springer Journals Preview Service: CC 1994, Springer-Verlag Berlin Heidelberg New York. CC All rights reserved. ------------------------------ From: Kearfott R. Baker Date: Wed, 23 Nov 1994 09:52:04 -0600 Subject: Contents: Interval Computations; Interval Computations. - 1994. - N 1. - 116 p. CONTENTS Mathematical Research G. Alefeld and G. Mayer A Computer Aided Existence and Uniqueness Proof for an Inverse Matrix Eigenvalue Problem 4 W. J. Luther and W. Otten Verified Inclusion for Eigenvalues of Hill's Equation 28 G. L. Kozina and V. A. Perepelitsa Interval Spanning Trees Problem: Solvability and Computational Complexity 42 H. Schwandt Suboptimal Enclosures for the Interval Buneman Algorithm for Arbitrary Block Dimension 51 O. B. Ermakov Solving Systems of Ordinary Differential Equations Using Adams' Interpolation Method with Guaranteed Accuracy 90 Teaching G. G. Menshikov On Different Definitions of Interval Extension: Problems of Teaching 96 Amendment 99 Bibliography Bibliography of Soviet Works on Interval Computations. Part V 100 Requirements for manuscript preparation 110 Requirements for manuscript preparation (in Russian) 111 Addresses of the editorial board members 112 Contents 114 OTHER NEWS: An updated preliminary program, as well as registration and hotel reservation forms for the International Workshop on Applications of Interval Computations have been placed in the anonymous ftp area of interval.usl.edu ------------------------------ From: Ake Bjorck Date: Wed, 23 Nov 94 17:24:22 +0100 Subject: Contents, BIT CONTENTS BIT Volume 34, No. 4 (1994) ISSN 0006-3835 Modeling and velocity stabilization of constrained mechanical systems Taifun Alishenas and \"Orn {\'O}lafsson, pp. 455--483 Finding minimum height elimination trees for interval graphs in polynomial time Bengt Aspvall and Pinar Heggernes, pp. 484--509 An implicit shift bidiagonalization algorithm for ill-posed problems {\AA}ke Bj\"orck, Eric Grimme, and Paul Van Dooren, pp. 510--534 On the convergence of the multivariate ''homogeneous'' QD-algorithm Annie Cuyt, pp. 535--545 Theoretical and practical efficiency measures for symmetric interpolatory quadrature formulas Paola Favati, Grazia Lotti, and Francesco Romani, pp. 546--557 Least squares fitting of circles and ellipses Walter Gander, Gene H. Golub, and Rolf Strebel, pp. 558--578 Preconditioning strategies for asymptotically ill-conditioned block Toeplitz systems Stefano Serra, pp. 579--594 Acknowledgements of referees p. 595 Index Volume 34 pp.596--598 BIT now accepts papers in LaTeX. For information send email to the Editor: {\AA}ke Bj\"orck Department of Mathematics Link\"oping University S-581 83 Link\"oping, Sweden E-mail: akbjo@math.liu.se FAX: +46-13 100 746 ------------------------------ End of NA Digest ************************** -------