Subject: NA Digest, V. 93, # 13 NA Digest Sunday, March 28, 1993 Volume 93 : Issue 13 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: The L(D**(-1),U) Decomposition. Reply about Fitting Experimental Data Snow Avalanche Info Needed Finite Element Codes with Message Passing MGGHAT Now Available Change of Address for Volker Mehrmann Pacific Northwest Dynamical Systems Seminar Bay Area NA Day Symposium in Honour of Leslie Fox Numerical Analysis and Dynamical Systems Nonlinear Numerical Methods and Rational Approximation National Information Infrastructure Final Call for Papers: JPDC special issue Contents, Numerical Algorithms Contents, Journal of Computational and Applied Mathematics 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: Ned Anderson Date: Mon, 22 Mar 93 07:25:11 PST Subject: The L(D**(-1),U) Decomposition. High Performance Computing: Using an L(D**(-1),U) decomposition. This note proposes the use of a modified approach to information storage in the LU decomposition process for solving linear systems. This approach has significant practical value, particularly in the solution of tridiagonal or other banded systems. Simply stated, the proposal is to, at each elimination step: 1. Use the reciprocal of the current pivot element to do the elimination (this is already a common technique). 2. Store this reciprocal (of the diagonal element of U) in place of the diagonal element itself. I propose we call this approach the L(D**(-1),U) decomposition. This lets us replace the N floating divides in the back solve by N multiplies. Its value derives from the fact that on many machines, divides are much slower than multiplies, and/or are not part of the pipelined arithmetic unit. Here is a code segment (cf. xGTSV in LAPACK) implementing the proposed approach for a tridiagonal solver (with no pivoting or storage of L): D( 1 ) = ONE / D( 1 ) DO K = 1, N - 1 MULT = DL( K ) * D( K ) D( K+1 ) = D( K+1 ) - MULT*DU( K ) B( K+1 ) = B( K+1 ) - MULT*B( K ) D( K+1 ) = ONE / D( K+1 ) END DO * D**(-1),U and (L**(-1))B calculations complete. * * Back solve: B( N ) = B( N ) * D( N ) DO K = N - 1, 1, -1 B( K ) = ( B( K )-DU( K )*B( K+1 ) ) * D( K ) END DO This code yielded a 50% improvement in the Mflop rate (over the traditional algorithm) on a DEC Alpha AXP 150 Mhz machine. For full matrices and LAPACK, one may want to consider modifying xGETF2 to store reciprocal pivots, and modifying the BLAS3 routine xTRSM to accept a third value, 'reciprocal' for the DIAG parameter which now accepts either 'unit' or 'nonunit'. -- Dr. Ned Anderson, Digital Equipment Corporation, (508)467-4862 3/3/93 [Editor's Note: It should be mentioned that this approach is slightly less accurate and robust. Consider the 1-by-1 case. Solve 7*x = 21. Computing x = 21/7 = 3 gives the exact answer, while computing x = 7**(-1)*21 = (.142857...)*21 might not give an exact 3. Moreover, some pivots, near the under- or overflow limits, cannot be reciprocated. But, neither is these points is actually very important. If you want speed, avoid divisions.] ------------------------------ From: Grace Wahba Date: Mon, 22 Mar 93 12:02:37 -0600 Subject: Reply about Fitting Experimental Data In response to C. Zhu concerning fitting experimental data by best approximation, see my book `Spline Models for Observational Data' SIAM 1990 and 13 pages of references cited there. (Order info may be found by ftp at ftp.stat.wisc.edu in pub/wahba/bkinfo). He might also want to look at the literature on minimax estimation in the statistical literature. ------------------------------ From: John Prentice Date: Wed, 24 Mar 93 17:41:37 MST Subject: Snow Avalanche Info Needed This question is more a physics question than a computing or mathematics question, but since this newsletter goes to a very diverse group of people, I thought I would submit it anyway and see if anyone has any thoughts. I am doing some research into the solid/fluid mechanics of snow avalanches, particularly avalanches in the continental region of the US Rockies. To carry out my research program, I need to find out just about everything that is known about the constitutive properties and physics of snow, particularly highly porous snow such as we get in this region. I also need to find out what is known about the constitutive properties and physics of hoar depth and phase transitions in snow in general. If anyone has any references, pointers, or recommendations for who to ask, I would much appreciate it. I am also trying to dig up any books or articles on the general physics of snow avalanches. Any recommendations for that would also be much appreciated. John Dr. John K. Prentice Quetzal Computational Associates 3200 Carlisle N.E., Albuquerque, NM 87110-1664 USA Phone: 505-889-4543 E-mail: quetzal@aip.org -or- jkprent@cs.sandia.gov ------------------------------ From: Stefano Foresti Date: Thu, 25 Mar 1993 15:00:28 -0700 Subject: Finite Element Codes with Message Passing We are interested in public domain finite element codes that have been developed for distributed memory parallel computers with message passing software (for instance Intel, PVM, Parasoft Express, etc.). Any information is appreciated. Stefano Foresti and Dave Barker Utah Supercomputing Institute 85 SSB University of Utah Salt Lake City, Utah 84112, USA tel: (801)581-3173 Fax: (801)585-5366 E-mail: stefano@osiris.usi.utah.edu E-mail: ibmdeb@osiris.usi.utah.edu ------------------------------ From: Bill Mitchell Date: Fri, 26 Mar 93 10:49:54 EST Subject: MGGHAT Now Available MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations of the form: -( p * u ) -( q * u ) + r * u = f in omega x x y y u = g on boundary 1 of omega u + c * u = g on boundary 2 of omega n where p,q,r,f,c and g are functions of x and y, omega is a polygonal domain in R2, n is the outward unit normal, and boundaries 1 and 2 form a partition of the boundary of omega. This program is now available for public use. It uses a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Windows display, and a posteriori through output files that can be used as GNUPLOT input. The user supplies subroutines containing the coefficient functions p, q, r, f, c, and g, a subroutine with the inital (coarse grid) triangulation to define the domain, and a main program that sets program parameters and calls subroutine mgghat. The program is mostly FORTRAN 77, but uses C for the X11 graphics (can be disabled). MGGHAT is available from netlib. Send the message "send index from pdes/mgghat" to netlib@research.att.com. MGGHAT can also be obtained from MGNET (multigrid network) by annonymous ftp to casper.cs.yale.edu in directory mgnet/mgghat. Enjoy! -- Bill William F. Mitchell | wmitchell@atl.ge.com GE Advanced Technology Labs | na.mitchell@na-net.ornl.gov Bldg. 145-2 Moorestown Corp. Center | Voice: (609) 866-6536 Moorestown, NJ 08057 | Fax: (609) 866-6397 ------------------------------ From: Volker Mehrmann Date: Tue, 23 Mar 93 14:15:42 MET Subject: Change of Address for Volker Mehrmann On April 1, 1993 I will move to Chemnitz and my new address will be Volker Mehrmann Fachbereich Mathematik Technische Universitaet Chemnitz-Zwickau Reichenhainer Str. 41 D-0-9022 Chemnitz Tel. (049) (0)371-561-2659 (office) (049) (0)371-561-2657 (fax) email: mehrmann@mathematik.tu-chemnitz.de ------------------------------ From: Edoh Y. Amiran Date: 26 Mar 1993 14:02:07 -0800 (PST) Subject: Pacific Northwest Dynamical Systems Seminar The Pacific Northwest Dynamical Systems Seminar will be held at Western Washington University in Bellingham, WA, on April 17-th. The speakers are: M. Gerber (U. IN), F. Diacu (U. Vic.), D. Chalice (WWU), S. Tuncel (UW), E.S. VanVleck (SFU), and K. Lu (BYU). The talks will be held at Parks Hall 164 from 9:00 to 5:00. For more information e-mail edoh@wwu.edu or write to Edoh Amiran, Mathematics, WWU, Bellingham WA, 98225-9063. -- Edoh Y. Amiran ------------------------------ From: Gene Golub Date: Sat, 27 Mar 93 17:25:51 PST Subject: Bay Area NA Day ANNUAL BAY AREA NA DAY The annual Bay Area NA Day will take place at Stanford on Sat, April 10, beginning at 9:30 am. The meeting will take place in History Corner. The speakers will include Alan Edelman, Vince Fernando, John Strain, Andrew Stuart and several graduate students from Berkeley and Stanford. There will be a reception at Gene Golub's house followed by a Chinese banquet; the cost is $20 per person. All interested persons are welcome. Please send me a note by April 7 if you are interested in attending, and participating in the dinner. For further information, call me at (415) 723-3124 or send an e-mail msg. Gene Golub ------------------------------ From: Nancy K. Nichols Date: Wednesday 24th March 1993 18:17:31 GMT Subject: Symposium in Honour of Leslie Fox A SYMPOSIUM IN HONOUR OF LESLIE FOX together with the SIXTH LESLIE FOX PRIZE COMPETITION is to be held JUNE 24 - 25, 1993 Mathemtatical Institute, Oxford University OXFORD, UK The symposium is being held to celebrate the many contributions of Leslie Fox to the research, teaching and applications of numerical analysis. The programme includes: on Thursday, June 24, the finals of the Sixth Leslie Fox Prize Competition and the award of the prizes by Clemency Fox. An invited lecture by Professor G.H. Golub is to follow. On Friday, June 25, invited talks on topics in numerical analysis are to be presented by friends and colleagues associated with different stages of Leslie's career, from schooldays through retirement. Speakers include: Dr. D. Kershaw, Professor C. Clenshaw, Professor J. Walsh, Dr. A. Tayler, Dr. D. Mayers, Dr. N.I.M. Gould, and Professor A. Stuart. A sherry reception and honorary dinner are to be held in Balliol College on the evening of Thursday, June 24. All friends are welcome at the dinner (including those not participating in the scientific programme). Registration fees for the conference are: Two day programme: #40 including lunches in Balliol College, morning and afternoon coffee/tea and sherry reception (#20 for students) Fox Prize day only: #20 including lunch, coffee/tea and reception (#10 for students) Conference Dinner: #26 (including wine) for participants #30 (including reception and wine) for non-participants Accomodation for a limited number of participants is to be available in Balliol College at a rate of #19.40 per person for bed and breakfast. Information on other accomodation can be obtained from the symposium organizers. Any funds raised from the meeting are to be contributed to the Leslie Fox Prize Fund. Additional donations to the capital fund are welcome at any time. Cheques should be made payable to the Secretary, IMA, 16 Nelson Street, Southend-on-Sea, Essex SS1 1EF, UK. Local Organizers: Prof. K.W. Morton (Chairman), Dr. N.K. Nichols, Dr. D. Mayers, Prof. S. Hammarling, Prof. I.S. Duff Fox Prize Adjudicators: Dr. N.K. Nichols (Chairman), Prof. C.M. Elliott, Prof. C.T.H. Baker Those planning to attend the symposium are encouraged to register as soon as possible. Correspondence, including a request for an electronic registration form, should be addressed to either: Professor K.W. Morton Dr. N.K. Nichols Oxford University Department of Mathematics Computing Laboratory University of Reading 8/11 Keble Road Box 220 Oxford OX1 3DQ UK Reading RG6 2AX UK Tel. +44 865 273885 Tel. +44 734 318988 FAX +44 865 273839 FAX +44 734 313423 email: email: Joan.Himpson@uk.ac.oxford.comlab na.nichols@na-net.ornl.gov n.nichols@uk.ac.reading ------------------------------ From: A. Spence Date: Fri, 19 Mar 93 15:31:41 GMT Subject: Numerical Analysis and Dynamical Systems LONDON MATHEMATICAL SOCIETY TWO DAY MEETING THURSDAY -- FRIDAY 13--14 MAY 1993 UNIVERSITY OF CAMBRIDGE Numerical Analysis and Dynamical Systems Thursday 2.00 Opening Session 2.10 C. Foias (Bloomington, Indiana): ``Interpolation theory and the localization of the global attractor'' 3.45 C. Grebogi (College Park, Maryland): ``Shadowing in chaotic systems'' 5.00 D. Watkins (Seatle, Washington): ``A numerical analyst's view of isospectral flows'' Friday 10.15 R.D. Skeel (Urbana-Champaign, Illinois): ``Symplectic integration with multiple time steps and variable step size'' 12.00 C.M. Elliott (Sussex): ``Dynamical phase transitions and parabolic equations'' 2.30 E. Doedel (Caltech): ``On algorithms and software for bifurcation problems'' 3.30 Meeting closes The lectures will be held at the Mill Lane Lecture Rooms, (opposite DPMMS) Cambridge. All interested are very welcome. A dinner will be held at The University Centre on the evening of Thursday 13th May at 8.00pm. The cost of the dinner will be 18.50 pounds per person, inclusive of wine. Those wishing to attend should inform A. Iserles, DAMTP, Silver Street, Cambridge CB3 9EW, enclosing a cheque payable to ``University of Cambridge'', to arrive by 7th May. Enquiries may be addressed to A. Iserles, DAMTP, Silver Street, Cambridge, CB3 9EW (email A.Iserles@uk.ac.cam.amtp) or A. Spence, School of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY (email as@uk.ac.bath.maths). ------------------------------ From: Annie Cuyt Date: Thu, 25 Mar 93 14:53:15 +0100 Subject: Nonlinear Numerical Methods and Rational Approximation CONFERENCE ANNOUNCEMENT Nonlinear Numerical Methods and Rational Approximation Organiser: A. Cuyt (UIA, Antwerp). Scientific Committee: A. Bultheel (KUL, Leuven), A. Cuyt (UIA, Antwerp), J. Meinguet (UCL, Louvain-la-Neuve), J.-P. Thiran (FUN, Namur). UPON GENERAL REQUEST THE DEADLINE FOR REGISTRATION IS EXTENDED TO MAY 1. SINCE I AM ALSO ABROAD IN APRIL, THERE WILL BE NO REPLY TO ANY REQUESTS FOR INFORMATION IN THAT PERIOD. Invited Speakers: A. Gonchar (Moscow), M. Gutknecht (Zurich), W. B. Jones (Boulder, USA), D. Lubinsky (Witwatersrand, S-Africa), E. Saff (Tampa, USA). In 1993 another conference will be organised on the use of rational functions in different fields of numerical analysis. It will take place at the University of Antwerp (UIA) from September 5 to 11. The registration fee of 7 500 Bf will cover participation, lunch and dinner on campus, all social events, coffee-breaks, transportation from and to town and a copy of the conference proceedings. Since Antwerp is in 1993 Europe's cultural capital, special attention will be paid to housing and social events for the participants. Registration should be made before April 1 on the enclosed form. Each of the following sessions will be introduced by a one-hour survey lecture. All other participants are invited to present a 20-minute research talk. Abstracts should be mailed together with the registration form before April 1. Proceedings will be published by Reidel just like in 1987. Only papers received in their final form by September 30 can be considered for publication. Details for the preparation of a manuscript shall be mailed to all registered participants after June 1. Sessions: The emphasis will be on Pade approximation, Rational interpolation, Rational approximation, Continued fractions and Orthogonal polynomials. For each of those topics we also welcome all Multivariate and Multidimensional problems, Applications, Error analysis and Software development. Further Information: Annie Cuyt, Dept of Mathematics and Computer Science, University of Antwerp (UIA), Universiteitsplein 1, B-2610 Wilrijk-Antwerp, Belgium, tel: (32) 3/820.24.07, fax: (32) 3/820.24.21, secr: (32)3/820.24.01, e-mail: cuyt@wins.uia.ac.be ------------------------------ From: Karen Friedman Date: Tue, 23 Mar 93 16:26:06 MST Subject: National Information Infrastructure INFORMATION EXCHANGE TELECOMMUNICATIONS AS PART OF THE NATIONAL INFORMATION INFRASTRUCTURE You are cordially invited to attend the IEEE-USA Information Exchange on Telecommunications as Part of the National Informa- tion Infrastructure. The United States needs to develop a world-class national infor- mation infrastructure. Fundamental to achieving this goal is establishing a national telecommunications policy that fosters effective application of evolving technologies, incentives for investment, and responsiveness to users. Many groups and associ- ations are initiating projects to represent the views of their members on such an infrastructure. Because IEEE's wide-ranging membership touches almost all enti- ties addressing this issue, the IEEE Committee on Communications & Information Policy will convene an Information Exchange May 4-5, 1993 Rosslyn Westpark Hotel Arlington, Virginia The purpose of this exchange is to allow the groups and associa- tions developing a vision of U.S. information infrastructure to share views and better understand their respective issues. We envision a dialogue among those already active in this arena and other key individuals who are directly concerned with telecommun- ications. This will be a neutral ground where different interests can target particular issues important to them and this country. Panelists of national stature will cover the range from technology through policy. We expect many officials of the Exe- cutive and Legislative branches to participate as well. The ultimate goal of this effort is to bring together the ele- ments for a national policy to guide the nature and continuing development of a superior infrastructure. This Information Exchange is a first step in the process. Attendance is limited. The conference fee of $150.00 and the completed registration form are due by April 15. A block of rooms has been reserved in the name of "IEEE" at a discounted rate of $87.00. Hotel reservations must be made directly with the hotel at [PHONE (703) 527-4814; FAX (703) 522-8864] or before April 3, 1993. For registration and housing information, and a copy of the advance program, please contact: Deborah Rudolph Manager, Technology Policy Council IEEE-USA 1828 L Street NW, Suite 1202 Washington, DC 20036 PHONE: (202) 785-0017 FAX: (202) 785-0835 ------------------------------ From: Xian-He Sun Date: Mon, 22 Mar 93 21:34:54 -0500 Subject: Final Call for Papers: JPDC special issue CALL FOR PAPERS Special Issue of the Journal of Parallel and Distributed Computing on Scalability of Parallel Algorithms and Architectures. Papers are solicited for a special issue of the Journal of Parallel and Distributed Computing on scalability of parallel algorithms and architectures planned for April 1994. The issue will publish about eight regular papers (about 35 double-spaced manuscript pages) and upto four research notes (about 15 double-spaced manuscript pages). The objective of this special issue is to bring together the research done by theoreticians, application developers, and designers of architectures and system software on scalability analysis of large- scale parallel systems. Topics of interest include but are not limited to Scalability metrics, Scalability analysis of parallel algorithms, applications, and architectures, Cost effectiveness of scaling parallel architectures in terms of performance, Software tools for scalable parallel systems. Authors should follow the JPDC manuscript format as described at the end of each JPDC issue. Five copies of complete manuscript should be sent to one of the guest editors by April 5, 1993. The authors will be notified of the decision by September 1, 1993 and the final manuscript ready for publication will be due by October 1, 1993. Guest Editors: Prof. Vipin Kumar Dr. Xian-He Sun Department of Computer Science ICASE 200 Union Street S.E., Rm. 4-192 Mail Stop 132C University of Minnesota NASA Langley Research Center Minneapolis MN 55455 Hampton, VA 23681-0001 Tel: (612) 624-8023 Tel: (804) 864-8018 Fax: (612) 625-0572 Fax: (804) 864-6134 Email: kumar@cs.umn.edu sun@icase.edu ------------------------------ From: Daniel Baltzer Date: Mon, 22 Mar 1993 16:07:21 -0700 Subject: Contents, Numerical Algorithms Contents NUMERICAL ALGORITHMS Editor-in-Chief: Claude Brezinski, Laboratoire d'Analyse Numerique et d'Optimisation, UFR IEEA - M3, Universite de Lille 1, France, fax: +33 - 20 43 49 95, e-mail: brezinsk@frcitl81.bitnet Numerical Algorithms, Volume 3 (1993), issues 1-4: Moment problem formulation of the Schrodinger equation, D. Bessis and C. R. Handy. Extrapolation methods in numerical integration, P. Rabinowitz A reliable modification of the cross rule for rational Hermite interpolation, B. Beckermann and C. Carstensen. A uniform approach for Hermite Pade and simultaneous Pade approximants and their matrix-type generalizations, B. Beckermann and G. Labahn. Interpolatory integration rules and orthogonal polynomials with varying weights, T. Bloom, D.S. Lubinsky and H. Stahl. Para-orthogonal Laurent polynomials and associated sequences of rational functions, C.M. Bonan-Hamada, W.B. Jones, W.J. Thron and A. Magnus. Some vector sequence transformations with applications to system of equations, C. Brezinski and H. Sadok. A Favard theorem for orthogonal rational functions on the unit circle, A. Bultheel, P. Gonzalez-Vera, E. Hendriksen and O. Njastad. A moment problem associated to rational Szego functions, A. Bultheel, P. Gonzalez-Vera, E. Hendriksen and O. Njastad. Orthogonal rational functions and quadrature on the unit circle, A. Bultheel, P. Gonzalez-Vera, E. Hendriksen and O. Njastad. Rational approximants to symmetric formal Laurent series, M. Camacho and P. Gonzalez-Vera. Rational interpolation with a single variable pole, J. M. Carnicer. The Neville-Aitken formula for rational interpolants with prescribed poles, C. Carstensen and G. Muhlbach. Rational approximations for the cosine function: P-acceptability and order, J.P. Coleman. Multivariate rational data fitting: general data structure, maximal accuracy and object orientation, A. Cuyt and B. Verdonk. Implementation of the recurrence relations of biorthogonality, Z. Da Rocha. Convergence of simultaneous Hermite-Pade approximants to the n-tuple of q-hypergeometric series, M. G. de Bruin, K.A. Driver and D.S. Lubinsky. Bivariate Hermite-Birkhoff interpolation and Vandermonde determinants, M Gasca and J.J. Martinez. Matrix orthogonal Laurent polynomials and two-point Pade approximants, C. Gonzalez-Concepcion, P. Gonzalez-Vera, and E. Hendriksen. On extrapolation of Jagerman and Stetter rules, S. Gonzalez-Pinto, P. Gonzalez-Vera and J.C. Santos. Solution of integral equations using function-valued Pade approximants II, P.R. Graves-Morris and R. Thukral Rational approximation to Neumann series of Bessel functions, N. Hayek, P. Gonzalez-Vera and F. Perez-Acosta. A Levin-type algorithm for accelerating the convergence of Fourier series, H.H.H. Homeier. Asymptotics for Szego polynomial zeros, W.B. Jones, O. Njastad and H. Waadeland. Evaluation of a rational function, A.G. Law, C.N. Zhang, A. Rezazadeh and L. Jodar. The quadratic convergence of the topological epsilon algorithm for systems of nonlinear equations, H. Le Ferrand. Quadratic decomposition of orthogonal polynomials: a matrix approach, F. Marcellan and G. Sansgire. Two-dimensional orthogonal polynomials, their associated sets and the co-recursive sets, P. Maroni. Convergence and acceleration properties for the vector e-algorithm, A.C. Matos. On the internal stepsize of an extrapolation algorithm for IVP in ODE, M.Murofushi and H. Nagasaka. Extrapolation methods for some singular fixed point sequences, N. Osada. On higher order Pade-type approximants with some prescribed coefficients in the numerator, M.A. Pinar and T.E. Perez. Particular rules for the O-algorithm, M. Redivo Zaglia. Clifford algebras and vector-valued rational forms II, D.E. Roberts. P.C.-fractions and Szego polynomials associated with starlike univalent functions, F. Ronning. Sobolev inner products and orthogonal polynomials of Sobolev type, A, Ronveaux. Asymptotic behaviour of iterated modified transforms on some slowly convergent sequences, P. Sablonniere. Numerical factorization of a polynomial by rational Hermite interpolation, T.Sakurai, H. Sugiura and T. Torii. On extending backwards positive definite sequences, F.H. Szafraniec. Global extrapolation with a parallel splitting method, X.-C. Tai. Limit period Schur algorithms, W.J. Thron. A general module theoretic framework for vector M-Pade and matrix rational interpolation, M. van Barel and A. Bultheel. Best choice of the pole for the Pade-type approximant of a Stieltjes function, J. van Iseghem. Interpolation between sequence transformations, E.J. Weniger. Requests for sample copies and orders are to be sent to J.C. Baltzer AG, fax: +41-61-692 42 62, e-mail: publish@baltzer.nl ------------------------------ From: Anastassiou Date: 25 Mar 93 12:15:07 CDT Subject: Contents, Journal of Computational and Applied Mathematics Journal of Computational and Applied Mathematics vol. 45, number 3, 3 May 1993 S.K. Bhatta and K.S. Sastri Symmetric spline procedures for boundary value problems with mixed boundary conditions C. Carstensen and M.S. Petkovic On iteration methods withoug dervatives for the simulataneous determination of polynomial zeros H. Le Ferrand Vector orthogonal polynomials and matrix series M.N. Mikhail and M.R. El-Tantawy Effect of the medium viscosity on soound propagation and attenuation in ducts M. Ganesh A BIE method for a nonlinear BVP J.M.-S. Lubuma Error estimates in projexctive solutions of the Radon equation J.A. Ferreira dn P. De Oliveira Convergence properties of numerical discretizations and regridding methods D.M. Timus Some further results on the Hubbell rectangular source integral W. Layton Optimal difference schemes for 2-D transport problems E.H. Kaufman Jr and G.D. Taylor Coupled constrained rational approximation Nguyen huu Cong Note on the performance of direct and indirect Runge- Kutta-Nystrom methods P.W. Hemker and J.-A. Desideri Convergence behavious of defect correction for hyperbolic equations M.K. Oberle, S.L. Scott, G.T. Gilbert, R.L. Hatcher and D.F. Addis Mellin transforms of a generalization of Legendre polynomials ------------------------------ End of NA Digest ************************** -------