Subject: NA Digest, V. 94, # 10 NA Digest Sunday, March 6, 1994 Volume 94 : Issue 10 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: Meta-discussion of NA Digest A Function Equation C-codes for GEVD and SVD Question on Numerical Methods for ODEs Iterative Least Squares Backwards Heat Equation Eigenvalue of Large, Banded Toepliz Matrices Stability of Recurrence A Matrix Eigenvalue Problem (Solution #1) A Matrix Eigenvalue Problem (Solution #2) A Matrix Eigenvalue Problem (Solution #3) Interpolation on a Square Grid (Solution) New Book from IEEE Press Multigrid Workshop In Australia Bay Area NA Day Positions at IBM Watson Research Center Ph. D. Scholarship in Norway Benin Conference in Nigeria Contents, SIAM Optimization Contents, Linear Algebra and its Applications 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: Michael C. Grant Date: Sat, 26 Feb 1994 16:26:53 -0800 Subject: Meta-discussion of NA Digest > From: Tom Scavo > Date: Sun, 20 Feb 94 11:53:03 -0800 > Subject: Re: A Meta-answer > I agree with Arne. An interactive forum along the lines of the > Usenet newsgroup sci.math.num-analysis would be more productive. Then why not read sci.math.num-analysis? I wish more people would actively participate in that newsgroup. I would hope that Usenet access is not a problem for .edu sites, at least. Perhaps similar newsgroups (or their equivalent) can be created on Compuserve, AOL, Prodigy, etc. etc., with their contents automagically shared. > In fact, I think NA Digest and sci.math.num-analysis would > benefit greatly from each other. I know that some mailing lists > are automatically gated into the appropriate newsgroup. Maybe > that could be done in the case of NA Digest. I, for one, would > welcome the change. sci.math.num-analysis is small enough that an automatic news-to-mailing-list gateway might be practical. Those people with mail readers that can automatically extract such messages from their inbox and move them to a separate folder for later perusal will find this quite convenient; MH has such a facility called 'slocal' that might work with other mail handlers (I haven't used it though). > Just look how long it's taken to get these three related messages > to the list. In a newsgroup, it's not uncommon for a thread to > generate the same reponse in a matter of hours. That's why this digest is much better suited for things such as conference announcements, employment positions, and other general interest announcements for which no feedback (to the Digest) is necessary. Michael C. Grant mcgrant@rascals.stanford.edu ------------------------------ From: Frank Stenger Date: Sun, 27 Feb 1994 11:35:19 -0700 Subject: A Function Equation An unsolved problem: Let f be a positive, decreasing function defined on [0,1], such that f(0) = 1, f(1) = 0, and such that for all x on [0,1], we have f((1 - (f(x))^2)^(1/2)) = 1-x, and f(f(x)) = x. Can we find an explicit functional expression for f? Frank Stenger Department of Computer Science University of Utah Salt Lake City, Utah 84112 E-mail: stenger@cs.utah.edu Phone: (801) 585-SINC Fax: (801) 581-5843 ------------------------------ From: Comon Pierre Date: Mon, 28 Feb 1994 11:03:28 GMT Subject: C-codes for GEVD and SVD Could anyone send me C-codes for GEVD and SVD. The library packages I have do not contain these tools. Thanks, comon@mimosa.unice.fr ------------------------------ From: Stanly Steinberg Date: Mon, 28 Feb 94 09:32:04 MST Subject: Question on Numerical Methods for ODEs I am looking for information on discretizations of a system of ordinary differential equations of the form dx/dt = A x + B x where the system with B = 0 is stiff and simple while the system for A = 0 is not stiff and complex. Stanly Steinberg stanly@math.unm.edu ------------------------------ From: James F. Epperson Date: Wed, 2 Mar 94 14:52:14 CST Subject: Iterative Least Squares Do there exist algorithms for solving sparse, structured least squares problems that are analogous to, say, SOR or Gauss-Seidel for the linear systems problem? What am looking for is a way to solve the normal equations (A^T)Ax=(A^T)f without forming (A^T)A, or to do an (approximate) QR decomposition of A without all the fill-in that would ordinarily occur. Thanks in advance Jim Epperson Mathematical Sciences Dept. Univ. of Alabama-Huntsville ------------------------------ From: James F. Epperson Date: Wed, 2 Mar 94 14:56:04 CST Subject: Backwards Heat Equation To save me and a colleague from the embarassment of perhaps re-inventing the wheel, could someone direct me to a reference for what might be considered the "state-of-the-art" for solving the backwards heat equation? Thanks in advance, Jim Epperson Mathematical Sciences Dept. Univ. of Alabama-Huntsville ------------------------------ From: Fred Kus Date: Fri, 4 Mar 1994 14:40:26 -0500 Subject: Eigenvalue of Large, Banded Toepliz Matrices Hi, A researcher here in Chemistry asked about software to solve for the extreme eigenvalues/vectors of a symmetric, narrow banded Toeplitz matrix of size n => 10**6. The band routines in Lapack as well as several Lanczos codes that were tried, did not seem suitable for such a large matrix. Also, they do not take advantage of the Toeplitz structure A(i,j) -> A(|i-j|) to reduce the memory required. Any information and/or software to deal with this problem would be greatly appreciated. Thanks Fred Fred W. Kus INTERNET: fred@mcmail.CIS.McMaster.CA Computing & Information PHONE: (905) 525-9140 ext. 24160 Services FAX (905) 528-3773 McMaster University A. N. Bourns Bldg. Rm 131C Hamilton, Canada L8S 4M1 ------------------------------ From: Simon Wang Date: Sat, 5 Mar 94 4:57 GMT Subject: Stability of Recurrence Stability of Recurrence Please help me consider the stability problem of the following recurrence: A X_{n+1} + B Y_{n+1} = C X_n + D Y_n (1) where A, B, C and D are known constant square matrices (nonsingular), Y and Z are vectors. My question is: if the following recurrences A X_{n+1} = C X_n (2) B Y_{n+1} = D Y_n (3) are stable, can we draw the conclusion that the recurrence in (1) must be stable? If so, any condition required? Thanks for your time. Simon Wang Email: MEG1839@V2.QUB.AC.UK ------------------------------ From: Garry Tee Date: Mon, 28 Feb 1994 12:35:09 +1200 Subject: A Matrix Eigenvalue Problem (Solution #1) >On Wed, 16 Feb 94 09:25 CST, Richard Luczak asked >in NA Digest, V. 94, # 8: > >> Let A be a tridiagonal matrix of the form >> -2 2 >> 1 -2 1 >> . . . >> 1 -2 1 >> 2 -2 >> What is the formula for all eigenvalues of matrix A? Let A be of order n>1. Consider the vector v[k] with elements v[k]_j = cos((k-1)(j-1)Pi/(n-1)), j = 1,...,n. It is readily verified that v[k] is an eigenvector of A with eigenvalue m_k = -4 sin^2((k-1)Pi/(2n-2)). (Note that v[k]_1 = 1, and hence v[k] is non-null). For k = 1,...,n this gives n distinct eigenvalues: 0 = m_1 > m_2 > ,,, > m_n = -4. Hence, those are all the eigenvalues of A, with eigenvectors v[1],,...v[k]. Garry J. Tee. Department of Mathematics, University of Auckland, Auckland, New Zealand. ------------------------------ From: Di Benedetto Date: Mon, 28 Feb 1994 17:14:57 GMT+1 Subject: A Matrix Eigenvalue Problem (Solution #2) On Wed, 16 Feb 94 09:25 CST, Richard Luczak asked in NA Digest, V. 94, # 8: > Let A be a tridiagonal matrix of the form > -2 2 > 1 -2 1 > . . . > 1 -2 1 > 2 -2 > What is the formula for all eigenvalues of matrix A? On Mon, 21 Feb 1994 12:35:37 --100, Christian Brechbuehler made in NA Digest, V. 94, # 9, the following conjecture: > Let A be n by n with n > 1. > Eigenvector j (not normalized) has the components > cos(i j Pi/(n-1)), > where 0 <= j < n > 0 <= i < n. > > Arbitrarily picking the first row of A, we have the Eigenvalues > 2(cos(j Pi/(n-1)) - 1). The conjecture is true, here is a possible way to prove it. Writing A = T - 2 I , it suffices to compute the eigensystem of the tridiagonal matrix 0 2 1 0 1 1 0 1 ..... T = ..... , ..... 1 0 1 1 0 1 2 0 which is Toeplitz except the first and the last row. The eigenvalue problem for T can be treated in a similar way as in W.F.Trench, "On the eigenvalue problem for Toeplitz band matrices" (Lin. Alg. Appl. 64, pp.199-214) by expressing the relation (T - l I) u = 0 as a difference equation: u(k+2) - l u(k+1) + u(k) = 0, k = 0,...,n-3 with the boundary conditions 2 u(1) = l u(0), 2 u(n-2) = l u(n-1). If z is a root of the characteristic equation z^2 - l z + 1 = 0 (whence l = z + 1/z) then u(k) has the expression u(k) = a1 z^k + a2 / z^k, where a1 and a2 are nonzero solutions of the linear system (2 z - l) a1 + (2/z - l) a2 = 0 z^(n-2) (2 - l z) a1 + z^(2-n) (2 - l/z) a2 = 0, which takes into account the boundary conditions. Substituting l = z + 1/z in the determinant d of such linear system and solving d = 0 with respect to z, the formulae conjectured by Brechbuehler are easily derived. Fabio Di Benedetto Dip. di Matematica - Univ. di Genova via L.B.Alberti 4 I - 16132 Genova (Italy) e-mail: dibenede@dima.unige.it ------------------------------ From: Katalin Balla <@helios.edvz.univie.ac.at,@HUEARN.SZTAKI.HU:H153Bal@HUELLA.BITNET> Date: 1 Mar 94 18:31:58 +0100 Subject: A Matrix Eigenvalue Problem (Solution #3) In Na-Digest 94, N9 , Christian Brechbuechler (brech@vision.ethz.ch) proposed a conjecture that answers the question posed by Richard Luczak (luczak@nag.com) a week earlier. The conjecture is true. > Let A be a tridiagonal matrix of the form > -2 2 > 1 -2 1 > . . . > 1 -2 1 > 2 -2 > What is the formula for all eigenvalues of matrix A? < 2(cos(j Pi/(n-1)) - 1). Date: Fri, 4 Mar 1994 13:56:07 +0100 (MET) Subject: Interpolation on a Square Grid (Solution) In last week's nanet-news T.R.Hopkins put forward a question concerning interpolation on a square grid, where the values of the function and its first order derivatives were known at the grid points. One possible solution is to find the unique interpolating polynomium of the form: p(x,y) = (a00+a10*x+a01*y+a11*x*y) + x^2*(a20+a30*x+a21*y+a31*x*y) + y^2*(a02+a12*x+a03*y+a13*x*y) on each square. The 12 coefficients are listed below in case of the square [0,1]x[0,1] and for the square [x1,x2]x[y1,y2] one may use p((x-x1)/(x2-x1),(y-y1)/(y2-y1)). a00=f11, (* the value of the function in (x1,y1) *) a10=fx11, (* the value of the x-derivative in (x1,y1) *) a01=fy11, (* the value of the y-derivative in (x1,y1) *) a11=fy21-f22+f12+f21-fx11+fx12-f11-fy11, a20=-2*fx11+3*f21-3* f11-fx21, a30=fx21+2*f11+fx11-2*f21, a21=-2*fx12+3*f22+3*f11-fx22+fx21+2*fx11-3* f21-3*f12, a31=fx12+fx22-fx21-fx11+2*f21-2*f11+2*f12-2*f22, a02=-2*fy11 -fy12-3*f11+3*f12, a12=-fy22+fy12+2*fy11-2*fy21-3*f12+3*f11+3*f22-3*f21, a03=-2 *f12+2*f11+fy12+fy11, a13=-fy12+2*f21-2*f11+2*f12-2*f22+fy21+fy22-fy11]); Jorgen Sand Dept. of Comp.Sci. Univ. of Copenhagen, Denmark e-mail: datjs@diku.dk ------------------------------ From: Rajni Patel Date: Sat, 26 Feb 1994 14:15:20 -0500 Subject: New Book from IEEE Press NEW from IEEE Press NUMERICAL LINEAR ALGEBRA TECHNIQUES FOR SYSTEMS AND CONTROL Edited by Rajni V. Patel, Concordia University Alan J. Laub, University of California, Santa Barbara Paul M. Van Dooren, University of Illinois, Urbana With an extensive 35-page introduction, and 21 pages of bibliography, this edited collection of 47 key papers incor- porates over 15 years of intensive research in the field of modern numerical linear algebra and its application to com- putational problems in systems and control. The book illus- trates the importance and rapid growth of this area of research, and helps to focus attention on the directions that future research should take. The introduction and papers presented in the book also provide a thorough back- ground for all current computer-aided control system analysis and design software and, in particular, address the following issues: * How to assess numerical stability and conditioning most effectively in numerical analysis. * Efficient ways to translate system and control ideas into reliable numerical algorithms. * Using condensed forms to check controllability, observability, and other properties of a model. * The effect of model uncertainties on various numer- ical properties of a given model. * The most reliable algorithms for the key computa- tional problems in linear system theory. As the only collection of papers covering the broad scope of numerical linear algebra in systems and control, this book will be of interest to engineers and applied mathematicians as well as others engaged in any aspect of control system analysis and design. The book contains the following chapters: 1. Introduction and Survey 2. General Numerical Issues in Control 3. Controllability, Observability, and Realizations 4. ``Closeness'' Problems 5. Frequency Response, Transfer Functions, Poles and Zeros 6. Pole Assignment and Observer Design 7. Riccati, Lyapunov, and Sylvester Equations 8. Some Relevant Results from Numerical Linear Algebra 9. Bibliography ORDERING INFORMATION: NUMERICAL LINEAR ALGEBRA TECHNIQUES FOR SYSTEMS AND CONTROL edited by Rajni V. Patel Alan J. Laub Paul M. Van Dooren IEEE Control Systems Society Member Price: $45.00 Regular IEEE Member Price: $72.00 List Price: $89.95 Hardcover, 736 pp IEEE Order #: PC0340-0 ISBN 0-7803-0443-8 The book can be ordered by telephone or fax: Tel: 1-800-678-IEEE (in USA) or 908-981-0060 Fax: 908-981-9667 or by mail: IEEE Customer Service Department 445 Hoes Lane, P.O. Box 1331 Piscataway, NJ 08855-1331 USA The book is also available at a slightly higher price from: IEEE Technical Activities Brussels Office 13, Avenue de L'Aquilon B-1200 Brussels BELGIUM Fax: 32.2.770.85.05 Phone: 32.2.770.22.42 ------------------------------ From: Steve Roberts Date: Mon, 28 Feb 94 14:54:25 +1100 Subject: Multigrid Workshop In Australia Workshop on Multigrid and Multilevel Methods School of Mathematical Sciences Australian National University 18th - 22nd April 1994 Profs Jim Bramble and Steve McCormick will both be at the ANU during the last two weeks of April. To take advantage of this opportunity, we are planning to hold a workshop in which they will be the major contributors. We plan to hold this workshop during the week 18th - 22nd April. Jim will give a series of talks describing some of his recent work on low regularity results for multigrid methods and Steve is planning to talk on algorithms and multigrid applications. Other speakers will include Zbigniew Leyk "Iterative methods for solving large nonsymmetric systems of linear equations" David Stewart "Multilevel methods for approximate inertial manifolds (in large scale dynamical systems)" Suely Oliveira "Parallel Multigrid for Mantle Convection" David Singleton "Multigrid in data parallel on the Connection Machine" Steve Roberts, "Multigrid methods applied to geometic evolution problems" A knowledge of the Multigrid method to the level of William Briggs' ``A Multigrid Tutorial'' will be assumed. It is intended that other participants to the workshop will have an opportunity to present their work on multigrid methods, or perhaps at a more informal level, present problems in which multilevel methods may be applied. At present the format and content of the workshop is very fluid. If you would like to attend the workshop, contact me (Steve Roberts, address below) giving details of your interests and background. We will try to arrange the main talks to suit the average background of the audience. The format of the workshop will be as informal as possible, with an emphasis on allowing interaction between the participants at the workshop. Steve Roberts Mathematics Department, The Faculties Office: (61)(6) 249 4445 Australian National University Messages: (61)(6) 249 2908 Canberra ACT 0200 Fax: (61)(6) 249 5549 AUSTRALIA E-mail: steve.roberts@maths.anu.edu.au ------------------------------ From: John Strain Date: Wed, 2 Mar 1994 09:15:54 -0800 Subject: Bay Area NA Day Bay Area Numerical Analysis Day at Berkeley Saturday, 26 March 1994 Everyone is invited!! Bay Area Numerical Analysis Day will be held on the UC Berkeley campus on Saturday, 26 March 1994. Young Bay Area numerical analysts will speak on their research. It will also be an excellent opportunity to meet colleagues. The meeting will begin at 9:30 am and finish up about 4:00, with a Chinese banquet at 6:30 pm, costing $20. A second announcement with details will follow shortly. -- John Strain ------------------------------ From: Erling Pytte Date: Fri, 4 Mar 94 10:01:25 EST Subject: Positions at IBM Watson Research Center The IBM T.J. Watson Research Center have several positions in the area of Computational Science. Intellectual power and scientific excellence are the primary criteria, but affinity for and ability to use parallel computers will be a valued tool. Among the resources available is a 128-way SP1 (128 RISC6000 with a fast switch for serial or parallel use). Applications with resumes, list of publications, and references should be sent to Dr. Erling Pytte, IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598. ------------------------------ From: Petter Bjorstad Date: Sat, 5 Mar 1994 11:16:22 +0100 Subject: Ph. D. Scholarship in Norway A Ph.D scholarship supported by the Norwegian Research Council, is available immediately. The Ph.D. student will perform research in scientific computing at the department's laboratory for parallel computing (Para//ab). The successful candidate must document strong knowledge in mathematics and computer science. For more information please contact: professor Petter E. Bj{\o}rstad, Institutt for Informatikk, H{\o}yteknologisenteret, Universitetet i Bergen, N-5020 Bergen. Phone: +47-55544171 E-mail: Petter.Bjorstad@ii.uib.no ------------------------------ From: John Pryce Date: Wed, 2 Mar 94 15:40 BST Subject: Benin Conference in Nigeria REPORT ON BENIN CONFERENCE, NIGERIA 1994 by John Pryce and Alastair Spence The 24th - 28th January 1994 saw the Sixth International Conference on Scientific Computing at the University of Benin (Uniben), Nigeria, directed as were the previous conferences by Professor Simeon Ola Fatunla, head of the department of Mathematics and Computer Science. It was attended by over fifty delegates from Nigeria and by eight overseas visitors. The organizing committee had chosen Parallel Computation as a main theme of the conference in view of its importance to the computational needs of the Nigerian oil industry. The venue was the main Auditorium of the university. The opening ceremony was attended by senior figures of the university and of the state government. Unlike previous conferences no representatives of Federal government were present - this was one sign of the unsettled political situation in the country. The keynote addresses included John Pryce on "Scientific computing - key to an enduring technology?" who emphasized that while computing is essential to high technology, teaching basic technical skills (what in the UK are generally called Do-It-Yourself) so that they are natural everyday activities of the ordinary man and woman, is vital to an enduring technology. Also Dr Chris Phillips gave a lucid and "low-tech" introduction to "What parallel computing is all about". Unfortunately Prof Ezeilo, President of the Nigerian Mathematical Society, and billed to give a keynote address, was unable to be present. The overseas visitors gave mainly survey talks on their specialist areas. Willy Govaerts (University of Gent, Belgium) spoke on Bordered Matrix Methods in studying Bifurcations of Large Dynamical Systems; Rolf Jeltsch (ETH, Zurich, Switzerland) on a Truly Multi-dimensional Scheme for the Euler Equations of Gas Dynamics; Choi-Hong Lai (University of Greenwich, UK) on Domain Decomposition Methods and Massively Parallel Processing; Marco Marletta (University of Leicester, UK) on Numerical Solution of Hamiltonian System Eigenvalue Problems; Chris Phillips (University of Newcastle, UK) on Parallel Implementation of Conjugate Gradient-Type Methods; John Pryce (RMCS, Shrivenham, UK) on Test Packages for Mathematical Software with a Sturm-Liouville Test Set as an example; Roger Sidje (Ivory Coast, and Irisa, Rennes, France) on Krylov Subspace Methods for Markov Processes; Alastair Spence (University of Bath, UK) on Eigenvalues of Block Matrices arising from Discretizations of the Navier Stokes Equations. The talks by local researchers were again mostly of high quality, and perhaps the best local talk was from Prof Mrs Oni of Ibadan theoretical physics department who tackled a difficult and important problem from the oil industry: of devising theoretically well-founded methods for extracting more information from seismic survey data than is done at present. It was good to see how many of the speakers were young. There was a welcome increase in the number of numerical methods that were backed up by numerical experiments and performance comparisons. The 'locally produced' talks included, as one would expect, a good proportion from Professor Fatunla's own school on methods for ODE's but went well beyond this to problems of control, mathematical programming, combustion theory and queuing theory. For the first time there were also (mainly expository) talks on mainstream computer science topics such as topological sorting and the timetabling problem. As usual, many final-year mathematics students came to form an enthusiastic addition to the audience, and also attended a Matlab tutorial, at which one woman student was heard to say "Mmm, I begin to like this package". A new feature was a four day Software Engineering Workshop held the week prior to the Conference. This was a fairly informal event at which Simeon Fatunla and John Pryce presented the basics of the engineering approach to software development, to an audience of around twenty, the majority being from commerce and industry. On the day following the workshop, Willy Govaerts gave a series of lectures on the theory and uses of numerical continuation and bifurcation computations. The need for such training had been emphasized at the 1992 conference. The workshop was full of discussion, interaction and controversy and a whole day was given over to delegates presenting their own experiences. Plans for a follow-up course with more professional facilities and course material are in hand. The conference booklet was professionally produced (it was interesting to see a general move from LaTeX to Wordperfect for document preparation) with abstracts and full names and addresses of participants. For the first time it also contained maps of Uniben, Benin City and Nigeria and also - a valuable addition - the membership of the local organization committees who put in many hours of work before and during the conference to make it run smoothly within tight constraints on budget and equipment. It is invidious to single out names but especially obvious to us visitors were the efforts of Dr David Igbafe of the reception committee, Dr Frank Otunta who chaired the latter, and of Dr Victor Aladesula who was on hand punctually each morning for nearly two weeks to transport us from our NNPC accommodation to the workshop and conference venue, as well as his wife who also gave freely of her time. Most of the overseas visitors (not all owing to lack of space) were accommodated courtesy of the Nigerian National Petroleum Corporation (NNPC) at its guesthouse, where we were very comfortable and the menu included grasscutter (a local animal related to the porcupine) and other varieties of "bush meat" on demand. We appreciated the unobtrusive and efficient service of the guesthouse reception staff. The local museum and art gallery, and the Palm Research Institute (and its palm wine) were sampled as usual, and the visitors explored the Benin city market with the help of local staff and their wives to negotiate for souvenirs. Comparing this with previous conferences one can report both good news and bad news. The bad news is that the prevailing political uncertainty and the apparent absence of a coherent policy for higher education continues to leave the universities in financial decline. One talented colleague from a neighbouring university told me how his campus had been without national grid electricity for six months of the last academic year owing to inability to pay its electricity bill. Obviously, in such straits, other necessities of academic life such as purchase of up-to-date international journals have become unattainable luxuries. The good news is that there is clearly a core of people who are determined to carry on come what may and who are extending their locally based activities. The last two conference Proceedings have been edited, typeset and printed locally. Professor Fatunla's text "Fundamentals of Fortran Programming" (see endnote) appeared in November, again typeset and printed locally. Marketed by the African arm of Oxford University Press it has already achieved a wide sale in Nigeria. Mr Kayode Ojoko, an entirely Nigeria-educated civil engineer and software writer who runs a successful engineering consultancy in Lagos, has demonstrated his structural analysis Software at the 1992 conference and returned this year to show the increasing range and sophistication of his products. Necessity as always is proving to be the mother of invention and it is from such local technical mastery and initiatives, as much as on any outside help, that the technological progress of Nigeria will be based. It remains for us on behalf of all the visitors to give our thanks to all those who gave us hospitality: to Professor Fatunla and his team for inviting us and for their hard work on our behalf; to the Vice Chancellor of the university and his staff for their support to the conference; to the Nigerian National Petroleum Corporation for accommodating us; and to the many staff and students who welcomed us so warmly. Endnote ======= Fundamentals of Fortran Programming by Simeon Ola Fatunla, Ada Jane Press, Benin City, Nigeria, Nov 1993, 460 pp, price 20 UK pounds or 30 US dollars Proceedings of Benin Conference 1988+1990 (combined), ed. Simeon Ola Fatunla, University of Ibadan Press plc, Jan 1992, 308 pp, price 18 UK pounds or 27 US dollars Proceedings of Benin Conference 1992, ed. Smeon Ola Fatunla, Ada Jane Press, Benin City, Nigeria, Jan 1994, 230pp, price 18 UK pounds or 27 US dollars These are availbale from Prof Fatunla, Head of Mathematics and Computer Science, University of Benin, P.M.B. 1154, Benin City, Nigeria. Telex: Nigeria (905)41365 UNIBEN NG John Pryce APPLIED & COMPUTATIONAL MATHS GROUP RMCS SHRIVENHAM SWINDON SN6 8LA, UK ------------------------------ From: SIAM Date: Mon, 28 Feb 94 10:03:37 EST Subject: Contents, SIAM Optimization SIAM J. ON OPTIMIZATION 4-2 MAY 1994 Line Search Procedures for the Logarithmic Barrier Function Walter Murray and Margaret H. Wright Superlinearly Convergent O( nL)-Iteration Interior Point Algorithms for Linear Programming and the Monotone Linear Complementarity Problem Kevin McShane Convergence Properties of a Class of Rank-two Updates Paul T. Boggs and Jon W. Tolle Can Parallel Branch and Bound Without Communication be Effective? Per S. Laursen Convergence Theory of Nonlinear Newton)Krylov Algorithms Peter N. Brown and Youcef Saad On the Resolution of Linearly Constrained Convex Minimization Problems Ana Friedlander, Jose Mario Martinez, and Sandra A. Santos On Optimization Problems with Variational Inequality Constraints J. V. Outrata Triangular Decomposition Methods for Solving Reducible Nonlinear Systems of Equations J. E. Dennis Jr., Jose Mario Martinez, and Xiaodong Zhang Extension of Hoffman's Error Bound to Polynomial Systems Xiao-Dong Luo and Zhi-Quan Luo Globally Convergent Inexact Newton Methods Stanley C. Eisenstat and Homer F. Walker An Interior Point Column Generation Method for Linear Programming Using Shifted Barriers John E. Mitchell Predictor-Corrector Methods for a Class of Linear Complementarity Problems Sanjay Mehrotra and Robert A. Stubbs ------------------------------ From: Richard Brualdi Date: Thu, 3 Mar 1994 07:07:22 -0600 (CST) Subject: Contents, Linear Algebra and its Applications Linear Algebra and its Applications Contents Volume 199 Leon Jay Gleser (West Lafayette, Indiana), Michael D. Perlman (Seattle, Washington), S. James Press (Riverside, California), and Allan R. Sampson (Pittsburgh, Pennsylvania) A Brief Biography and Appreciation of Ingram Olkin 1 T. Ando (Sapporo, Japan) Majorizations and Inequalities in Matrix Theory 17 Y. L. Tong (Atlanta, Georgia) Some Recent Developments on Majorization Inequalities in Probability and Statistics 69 Karl Mosler (Hamburg, Germany) Majorization in Economic Disparity Measures 91 James V. Bondar (Ottawa, Ontario, Canada) Comments on and Complements to: Inequalities: Theory of Majorization and Its Applications, by Albert W. Marshall and Ingram Olkin 115 Hector F. Miranda and Robert C. Thompson (Santa Barbara, California) Group Majorization, the Convex Hulls of Sets of Matrices and the Diagonal Element - Singular Value Inequalities 131 Khakim D. Ikramov (Waterloo, Ontario, Canada) A Simple Proof of the Generalized Schur Inequality 143 Steen A. Andersson (Bloomington, Indiana) and Michael D. Perlman (Seattle, Washington) A Characterization of Matrix Groups That Act Transitively on the Cone of Positive Definite Matrices 151 Markus Abt (Augsburg, Germany) A Note on the Product Correlation Rule 171 Srinivasa R. Arikati and Uri N. Peled (Chicago, Illinois) Degree Sequences and Majorization 179 Berthold Heiligers (Augsburg, Germany) Totally Nonnegative Moment Matrices 213 J. Ferrer, Ma I. Garcia, and F. Puerta (Barcelona, Spain) Differentiable Families of Subspaces 229 M*Ua Asuncion Beitia and Juan M. Gracia (Vitoria-Gasteiz, Spain) Local Behavior of Sylvester Matrix Equations Related to Block Similarity 253 R. B. Bapat and Subhash C. Kochar (New Delhi, India) On Likelihood-Ratio Ordering of Order Statistics 281 B. Mond and J. E. Pecaric (Bundoora, Victoria, Australia) Inequalities Involving Powers of Generalized Inverses 293 Jianming Miao and Adi Ben-Israel (New Brunswick, New Jersey) On IP-Approximate Solutions of Linear Equations 305 S. W. Drury (Montreal, Quebec, Canada) A Bound for the Determinant of Certain Hadamard Products and for the Determinant of the Sum of Two Normal Matrices 329 Ingo Althofer (Bielefeld, Germany) On Sparse Approximations to Randomized Strategies and Convex Combinations 339 H. K. Wimmer (Wurzburg, Germany) Roth's Theorems for Matrix Equations With Symmetry Constraints 357 M. Knott and C. S. Smith (London, England) On a Generalization of Cyclic Monotonicity and Distances Among Random Vectors 363 Alan Hoffman (Yorktown Heights, New York) and Uriel G. Rothblum (Haifa, Israel) A Proof of the Convexity of the Range of a Nonatomic Vector Measure Using Linear Inequalities 373 Russell Merris (Hayward, California) Degree Maximal Graphs Are Laplacian Integral 381 S. W. Drury (Montreal, Quebec, Canada) On a Theorem of Wielandt and the Compounds of Unitary Matrices 391 Xiao-Li Meng (Chicago, Illinois) and Donald B. Rubin (Cambridge, Massachusetts) On the Global and Componentwise Rates of Convergence of the EM Algorithm 413 Rafael Bru, Juana Cerdan, and Ana M. Urbano (Valencia, Spain) An Algorithm for the Multiinput Pole Assignment Problem 427 Author Index 445 Special Issues in Progress 1. Special Issue Honoring Marvin Marcus; special editors are Bryan E. Cain, Moshe Goldberg, Robert Grone, and Nicholas J. Higham. To appear as Volume 201, April 1, 1994. 2. Linear Systems and Control, Third Special Issue; special editors are A. C. Antoulas, P. A. Fuhrmann, M. L. J. Hautus, and Y. Yamamoto. Submission deadline: November 30, 1992. To appear as Volumes 203/204/205, May/June/July 1, 1994. 3. Special Issue Honoring Chandler Davis; special editors are Rajendra Bhatia, Shmuel Friedland, and Peter Rosenthal. Submission deadline: March 31, 1993. To appear as Volume 206, July 15, 1994. 4. Proceedings of the Third Conference of the International Linear Algebra Society at Pensacola; special editors are Dianne P. O'Leary, Leiba Rodman, and Helene Shapiro. Submission deadline: June 30, 1993. Details provided with the conference announcement. 5. Proceedings of the conference ``Matrices and Graphs'' in honor of John Maybee's 65th birthday, held at Boulder, Colorado, May 7, 8, 1993. Special editors: C. R. Johnson and J. R. Lundgren. Submission deadline: August 31, 1993. Details provided with the conference announcement. 6. Fourth Special Issue on Linear Algebra and Statistics; special editors are Jeffrey J. Hunter, Simo Puntanen, and George P. H. Styan. Submission deadline: June 30, 1993. Details in Volume 177, December 1992. 7. Proceedings of the workshop ``Nonnegative Matrices, Applications and Generalizations'' and the Eighth Haifa Matrix Theory conference held at Haifa, Israel, May 31-June 4 and June 7-June 10, 1993, respectively. Special editors: S. Friedland, D. Hershkowitz, and R. Loewy. Submission deadline: September 15, 1993. Details provided with the conference announcement. 8. Special Issue Honoring Miroslav Fiedler and Vlastimil Ptak; special editors are Wayne Barrett, Angelika Bunse-Gerstner, and Nicholas Young. Submission deadline: August 31, 1993. Details in Volume 179. 9. Proceedings of the Fourth Conference of the International Linear Algebra Society at Rotterdam; special editors are Harm Bart, Ludwig Elsner, and Andre Ran. Submission deadline November 30, 1994. Details provided with the conference announcement. 10. Special Issue Honoring J. J. Seidel: special editors are Aart Blokhuis, Willem H. Haemers, and Alan J. Hoffman. Submission deadline: August 30, 1994. Details in Volume 193, November 1, 1993. Special issues are available to individuals at a reduced rate. For further information, please contact Yusuf Guvenc, Journals Customer Service, Elsevier Science Inc., 655 Avenue of the Americas, New York, NY 10010; Tel. 212-633-3955; Fax 212-633-3990. Special Issues Vol. 199 ------------------------------ End of NA Digest ************************** -------