Subject: NA Digest, V. 93, # 47 NA Digest Sunday, December 19, 1993 Volume 93 : Issue 47 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: Penalty Methods Question Searching for C code for MemSys Algorithm Test Matrix Toolbox for Matlab 4 BibTex Database on Netlib Numerical Solution of Sturm-Liouville Problems Conference on Domain Decomposition Stochastic Modeling Workshop at Stony Brook Massively Parallel Computing and Applications Course on Iterative Methods in Leuven Research Positions at ICASE Chair Position at University of Virginia PostDoctoral Position at U. C. Davis Positions at The University of Queensland Position at Memphis State Contents: Parallel Processing Letters 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: James F. Epperson Date: Tue, 14 Dec 93 15:27:00 CST Subject: Penalty Methods Question For a new problem I am studying, I need to do a penalized least squares type of computation (excuse the pidgin notation; I don't speak TeX): min{ |b-Au|^2 + a|Ku|^2 } where A and K are square matrices, b is a known vector, u is the unknown vector, and a is the penalty coefficient. The |.| notation denotes the standard 2-norm. I can do the usual manipulations to get the normal equations for this problem, and hence get a solution, but I am not sufficiently familiar with this area to know if there is a different or better way. In particular, I would like to know if there are algorithms based on a QR or SVD factorization of the matrices A and K. Thanks in advance for any replies. Jim Epperson epperson@math.uah.edu ------------------------------ From: Bruno Besace Date: Thu, 16 Dec 1993 01:58:04 +0000 Subject: Searching for C code for MemSys Algorithm I'm looking for C code about MemSys algorithm (Maximum Entropy algorithm). Any and all advice welcome. Thanks in advance for your responses. You may reply to me personally. Bruno Besace. (bruno.besace@fnet.fr) ------------------------------ From: Nick Higham Date: Fri, 17 Dec 93 10:16:49 GMT Subject: Test Matrix Toolbox for Matlab 4 I am pleased to announce the release of version 2.0 of The Test Matrix Toolbox for Matlab. This is a major new release of the toolbox first released in July 1989 and published as Algorithm 694: A collection of test matrices in MATLAB. ACM Trans. Math. Soft., 17(3):289-305, September 1991. The toolbox is distributed as a Unix shar file, available by anonymous ftp from The MathWorks at Internet address ftp.mathworks.com (144.212.100.10) in directory pub/contrib/linalg as files testmatrix.sh - the M-files (shar file: `sh testmatrix.sh' to unshar. A directory testmatrix will be created containing the M-files in the toolbox. Try the demonstration file tmtdemo.m.) testmatrix.ps - the 76-page documentation (PostScript file) Note: The MathWorks ftp server has a special feature which enables you to type, for example, `get testmatrix.ps.Z'; the server will then compress the file before sending it (make sure you set binary mode first). The Test Matrix Toolbox for Matlab 4 contains a collection of test matrices, routines for visualizing matrices, and miscellaneous routines that provide useful additions to Matlab's existing set of functions. There are 58 parametrized test matrices, which are mostly square, dense, nonrandom, and of arbitrary dimension. The test matrices include ones with known inverses or known eigenvalues; ill-conditioned or rank deficient matrices; and symmetric, positive definite, orthogonal, defective, involutary, and totally positive matrices. The visualization routines display surface plots of a matrix and its (pseudo-) inverse, the field of values, Gershgorin disks, and two- and three-dimensional views of pseudospectra. Nick Higham Department of Mathematics University of Manchester higham@ma.man.ac.uk ------------------------------ From: Stefano Foresti Date: Tue, 14 Dec 1993 18:16:24 -0700 Subject: BibTex Database on Netlib I was thinking that it would be very nice to have a Nanet or Netlib bibliography database in BibTex, similar to what Craig Douglas has coordinated on MGNet. Such a service would allow to: - Find all references of a Nanet subscriber, as it is currently possible to find out information with the "WHO" command on Xnetlib. - Find references with a certain keyword. - Retrieve reference entries, that are complete and updated. There are two possible kinds of bibliography databases I can think of: 1) Each Nanetter submits a file containing the publications in Bibtex format of which he/she is (co-)author (i.e. his/her list of publication). This option would just require that each Nanetter be responsible for formatting his list and submit an update once new papers are published. 2) Each Nanetter submits a Bibtex database, and these references are added in the database by a coordinator. This requires that the entries be sorted, checked for multiplicity and so on. However, I have the impression that this kind of a database would require a lot of coordinating work. One of the issues to consider is the definition of a standard entry format. For instance, Craig Douglas has defined a standard format of the Bibtex entry label (to enforce unicity) as follows: > > > > For example, my dissertation's key from 1982 is > > CCDouglas_1982a > > The key for a book by Braess, Hackbusch, and Trottenberg from 1984 is > > DBraess_WHackbusch_UTrottenberg_1984a > Stefano Foresti Utah Supercomputing Institute 85 SSB University of Utah Salt Lake City, Utah 84112, USA Ph: (801)581-3173 Fax: (801)585-5366 E-mail: stefano@osiris.usi.utah.edu ------------------------------ From: John Pryce Date: Mon, 13 Dec 93 17:46 +0100 (BST) Subject: Numerical Solution of Sturm-Liouville Problems This news item is to announce the forthcoming publication of my book "Numerical Solution of Sturm-Liouville Problems" by John D Pryce, FIMA Lecturer, Software Engineering Group, Royal Military College of Science, Shrivenham, Swindon SN6 8LA, UK In the series "Monographs on Numerical Analysis", Oxford University Press, Dec 1993, 330 pages, line illustrations, Hardback 37.50 pounds sterling Sturm-Liouville Problems (SLPs) belong to an elegant area of mathematics, the spectral theory of differential operators, which motivated much of the development of analysis and linear algebra by Hilbert, Weyl, Titchmarsh et al. in the early 20th century. Since the early 19th century SLPs have been ubiquitous in applied mathematics, arising naturally from modelling in such fields as acoustics, waveguide theory, hydrodynamic stability, MHD, and neutron transport. They are also of vital interest to physicists since Schrodinger's equation in one dimension is of Sturm-Liouville form. The variety of interesting SL-related computations reflects this triple background. The range of numerical methods is correspondingly vast: since the 1920s, quantum physicists found Schrodinger eigenvalues by methods often angled to a particular problem, based on asymptotics and thus of limited accuracy; since the 1950s numerical analysis journals contain SLP algorithms, often accurate and efficient on a class of (usually regular) problem but hard to automate. General ODE boundary-value software solves SLPs, but inefficiently. Typically none of these approaches handle singular endpoints in a way that corresponds to the mathematical theory. It is worth developing methods to exploit SLPs' special features and to cope systematically with the variety of behaviour singular SLPs display. The book will help the scientist/engineer who wants simple methods for simple SLPs but needs to know their limitations and be pointed to the best current library software for harder problems. It is also for the numerical software specialist who wants a reference on good SLP algorithms, their theory, their implementation in the library codes and the resulting performance. The basic mathematical theory as it relates to algorithms is covered in some detail. A chapter on Further Topics sketches problems or methods lying just beyond the book's main theme. There are numerous problems. An appendix presents a standard list of Test Problems, and a Benchmark for software validation. Contents: Introductory background; Elementary theory of the classical SLP; Simple matrix methods; Variational methods; Shooting and the scaled Prufer method; Pruess methods; Singular SLPs (theory); Singular SLPs (numerical treatment); Computing and manipulating eigenfunctions; Computation of resonances; Further topics; Conclusion. A: Eigenvalues 0-50 of two problems of Paine; B: Test problems and benchmark; C: Available SL software. ------------------------------ From: Jinchao Xu Date: Sun, 12 Dec 1993 23:04:32 -0500 Subject: Conference on Domain Decomposition The Eighth International Conference on Domain Decomposition Methods will be held in Beijing, China during May 15-19, 1995. For further information, please contact: Prof. Zhong-Ci SHI Computing Center Academia Sinica PO Box 2719 Beijing 100080, CHINA Email: zcshi%bepc2@scs.slac.stanford.edu ------------------------------ From: Yuefan Deng Date: Tue, 14 Dec 93 10:14:34 EST Subject: Stochastic Modeling Workshop at Stony Brook STOCHASTIC MODELING A Joint Cornell/MSI -- Stony Brook Workshop January 19 -- 20, 1994 This workshop will emphasize applications of stochastic modeling. Stochasticity represents the unknown, uncertain, not understood, or excessively detailed fine scale aspects of a system. Most real systems of interest to technology have stochastic features. In many cases stochasticity is a central feature, essential for even the simplest accurate description of the system. Usually there are deterministic, non-random features as well, and there are also deterministic laws to govern the dynamic evolution of randomness. The resulting interaction between randomness and determinism leads to stochastic modeling, stochastic partial differential equations and stochastic signal processing. The purpose of this workshop is to bring together a representative sampling of the many (and highly diverse) applications, or instances in which stochastic modeling has an important role to play. An intended outcome is to identify points of interaction between theory and applications for stochastic modeling. Topics and Speakers (more to invite and to expect): 1. Stochastic Fluids: Turbulent Mixing ---- J. Glimm 2. Stochastic Fluids: Anomalous Dispersion and Geostatistics ---- Q. Zhang 3. Interacting Particle System ---- C. Mueller 4. Percolation or Dynamic Ising Models ---- H. Kesten 5. Monte Carlo Simulation ---- M. Mascagni 6. Speech Recognition and Signal Processing ---- D. Sun 7. Stochastic Models in Manufacturing ---- M. Sobel 8. Stochastic Systems Models ---- TBD 9. Application of Stochastic Modeling to Finance ----D. Weiss (To be confirmed) 10. Stochastic methods in image processing ---- TBD For information, call Ms. Terry Mills Department of Applied Mathematics and Statistics Center for Scientific Computing State University of New York at Stony Brook Stony Brook, NY 11794 516-6632-9125 mills@ams.sunysb.edu ------------------------------ From: H.J.J. te Riele Date: Thu, 16 Dec 1993 18:39:34 +0100 Subject: Massively Parallel Computing and Applications CWI - RUU SYMPOSIA ON MASSIVELY PARALLEL COMPUTING AND APPLICATIONS CALL FOR ABSTRACTS In 1993 - 1994, CWI (Centre for Mathematics and Computer Science Amsterdam) and RUU (University of Utrecht) are organising a series of Symposia on Massively Parallel Computing and Applications. As far as the computing part is concerned, we are interested in contributions on the optimization and analysis of generic numerical algorithms on massively parallel computers. In particular, we think of iterative methods for solving large sparse linear systems of equations and for finding eigenvalues and eigenvectors of large sparse linear systems, multigrid methods for various types of PDEs, parallel methods for the solution of ordinary differential equation, software tools for parallelization, etc. On the applications side, we seek contributions in fields where optimization and analysis of numeric and nonnumeric algorithms for massively parallel computers are instrumental for real progress. In particular, we think of environmental problems, number theory and cryptography, multiple-particle systems, chemical reactions, computational fluid dynamics, seismic problems etc. The following advisory board will assist in the selection of the Symposium programs: P. Aerts, Dutch National Computing Facilities Foundation NCF O. Axelsson, Catholic University Nijmegen L.O. Hertzberger, University of Amsterdam P.A.J. Hilbers, Royal Shell Laboratory Amsterdam P.J. van der Houwen, CWI and University of Amsterdam W. Loeve, National Aerospace Laboratory NLR N. Petkov, University of Groningen M. Rem, Technical University Eindhoven J.G. Verwer, CWI H. Wijshoff, University of Leiden P. De Wilde, Technical University Delft We intend to organise bi-monthly one-day meetings each of which will be centred around a class of numerical algorithms or around a coherent applications field. The first three meetings took place in 1993 and were devoted to: "Topics in environmental mathematics" (June 4, 1993), "Parallel numerical algorithms" (Sept. 24, 1993), "Computational number theory and cryptography" (Nov. 26, 1993). The next three meetings are scheduled in the first half of 1994, namely, Febr. 4, 1994, March 25, 1994, June 3, 1994. Refereed proceedings will be published. Abstracts of possible contributions are solicited now. Please send an abstract to Herman J.J. te Riele, CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands (email: herman@cwi.nl) and indicate your preference, if any, for one of the above three dates. The deadline for submission of abstracts is Jan. 14, 1994. Notification of acceptance of the abstracts for the first meeting will be sent by Jan. 21, 1994. and for the two subsequent meetings by Febr. 25, 1994. A limited budget is available for contributors from abroad to partially cover travel and lodging expenses. The organisers: H.J.J. te Riele (CWI) H.A. v.d. Vorst (RUU and CWI) ------------------------------ From: Dirk Roose Date: Fri, 17 Dec 1993 15:02:23 +0100 (MET) Subject: Course on Iterative Methods in Leuven Course on Recent Advances in Iterative Methods for Solving Algebraic Systems and Eigenvalue Problems Leuven, Belgium The lectures will be given in February - March 1994, in three sessions of two days each, starting on Thursday at 10 a.m. and ending on Friday at 4 p.m. All lectures will take place in the Auditorium of the Arenberg Castle, Kardinaal Mercierlaan, B-3001 Leuven-Heverlee. Participants from Belgian academic institutions are requested to pay a regis- tration fee of 4000 BF. For other participants the registration fee is 15000 BF. Registration forms can be obtained via anonymous ftp from ftp.cs@kuleuven.ac.be in directory pub/NumAnal-ApplMath/Announce , files course.ascii or course.tex . The organisers, Dirk Roose, K.U.Leuven Roland Keunings, U.C.L., Louvain-la-Neuve P R O G R A M Thursday and Friday 24 - 25 February 1994 H. Van der Vorst (Universiteit Utrecht, the Netherlands) (3h) Survey on iterative methods for solving linear systems and their implementa- tion on modern computer architectures R.W. Freund (AT&T Bell Laboratories, Murray Hill, USA) (3h) I. The Lanczos Process for Large-Scale Nonsymmetric Matrix Computations II. Quasi-Minimal Residual Iterations for Non-Hermitian Linear Systems and Applications K. Vuik (T.U.Delft, the Netherlands) (1.5h) Krylov subspace methods applied to the incompressible Navier-Stokes eqs. G. Degrez (Von Karman Institute for Fluid Dynamics, Belgium) (1h) Acceleration of multiblock solvers for the compressible Euler and Navier-Stokes equations by Krylov subspace methods Thursday and Friday 10 - 11 March 1994 O. Axelsson and M. Neytcheva (Universiteit Nijmegen, the Netherlands) (3h) I. Block diagonal and Schur complement preconditioners II. The algebraic multilevel iteration method III. Approximate inverses and their use in preconditioning methods R. Beauwens (Universite Libre de Bruxelles, Belgium) (1h) Conditioning analysis F.X. Roux (Onera, Chatillon, France) (3h) A survey of domain decomposition methods R. Keunings (U.C.L., Louvain-la-Neuve, Belgium) (1h) Domain decomposition methods for nonlinear finite element analysis Thursday and Friday 24 - 25 March 1994 Y. Saad (University of Minnesota, USA) (3h) The use of Krylov subspace methods in scientific computing I. Linear systems; II. Eigenvalue problems; III. Nonlinear equations and other applications Ch. Farhat (University of Colorado at Boulder, USA) (3h) Domain decomposition methods for time-dependent problems: I. Construction of coarse grid problems for unstructured meshes; II. Scalable solution of coarse grid problems and efficient solution of repeated systems; III. Application to fluid/structure coupled problems M. Geradin (Universite de Liege, Belgium) (1h) Application of domain decomposition methods to flexible multibody dynamics F. Dupret (U.C.L., Louvain-la-Neuve, Belgium) (1h) Numerical stability analysis of stratified coating flow by Lanczos method K. Meerbergen (K.U.Leuven, Belgium) (1h) Preconditioners for computing eigenvalues with largest real part ------------------------------ From: Piyush Mehrotra Date: Tue, 14 Dec 1993 13:11:56 -0500 Subject: Research Positions at ICASE Research Positions at ICASE The Institute for Computer Applications in Science and Engineering (ICASE) is seeking fresh PhDs for staff scientist positions in the following areas: a) systems software for parallel computers, b) performance and reliability analysis, and c) parallel numerical algorithms. The principal focus of the software research effort at ICASE is development of tools and environments for porting large scale scientific applications to parallel and distributed systems. The focus of the performance and reliability analysis research is development of algorithms and tools for the study and optimization of performance of complex computer systems, especially parallel and distributed systems. The focus in parallel numerical algorithms is the development and experimental investigation of scalable methods for computational fluid dynamics applications. In the software area we are looking for PhDs interested in collaborative research on runtime support systems, on compiler design and enhancements, on tools for distribution, mapping, and load balancing, and on tools for performance monitoring and prediction. In the performance and reliability analysis area we seek PhDs interested in tools and algorithms for high performance simulation, and for parallel mathematical performance and relability analysis. Current topics of interest in the algorithms area are multilevel iterative methods, domain decomposition iterative methods, problem decomposition and parallel mapping in the presence of adaptivity, and multidisciplinary optimization. Staff scientists appointments are usually made for two years, with the possibility of a third-year extension. ICASE is a non-profit research organization located at the NASA Langley Research Center in Hampton, Virginia. The institute offers excellent opportunities to computer science researchers for collaboration on complex and computationally intensive problems of interest to NASA. ICASE staff scientists have access to Langley's 66 processor Intel PARAGON, a Cray Y/MP, and internet access to many other parallel architectures. US citizens/permanent residents will be given *strong* preference. Please send resumes to: Director ICASE, MS 132C NASA Langley Research Center Hampton VA 23681 or by e-mail to positions@icase.edu ------------------------------ From: Lois Mansfield Date: Wed, 15 Dec 93 15:21:12 EST Subject: Chair Position at University of Virginia UNIVERSITY OF VIRGINIA DEPARTMENT OF APPLIED MATHEMATICS CHAIR The University of Virginia invites applications and nominations for the position of Chair, Department of Applied Mathematics. The Department, which is in the School of Engineering and Applied Science, has a full-time faculty of eleven, and has numerous active research programs grouped in three major areas: continuum mechanics, control theory, and numerical analysis/scientific computing. The Department offers B.S., M.S., and Ph.D. degrees in Applied Mathematics and is responsible for all undergraduate and graduate education in Applied Mathematics within the School of Engineering and Applied Science. Candidates for the position must have a Ph.D. degree and an outstanding record of research and scholarship in Applied Mathematics. Also, they must have a firm knowledge of the best programs in Applied Mathematics nationally and internationally. A clear commitment to academic leadership, teaching, and administration within an environment dedicated to engineering and applied science is expected. Women and ethnic minority candidates are encouraged to apply. Priority will be given to applications received by March 1, 1994. Applications should be sent to: Professor Paul Allaire Chair, Search Committee c/o Department of Applied Mathematics Thornton Hall University of Virginia Charlottesville, VA 22903-2422 The University of Virginia is an equal opportunity/affirmative action employer. ------------------------------ From: Elbridge Gerry Puckett Date: Thu, 16 Dec 93 14:33:24 PST Subject: PostDoctoral Position at U. C. Davis POSTDOCTORAL POSITION IN NUMERICAL ANALYSIS / COMPUTATIONAL MATHEMATICS Applications are invited for a Visiting Research Assistant Professorship in computational mathematics / numerical analysis at the University of California, Davis effective July 1, 1994. The appointment is for one year and is renewable up to two times for a total of three years. The salary will be commensurate with the successful applicant's qualifications. Applicants must have received a PhD by the date of the appointment and no earlier than three years prior to the appointment, and have an outstanding record or show great promise in teaching and research. Duties include undergraduate and graduate teaching and research. The teaching load is five quarter courses per year and may include an advanced course in the candidate's field. Applications will only be considered from individuals who have a strong background in numerical analysis and computational mathematics. The U. C. Davis Department of Mathematics includes faculty in both pure and applied mathematics engaged in numerous areas of mathematical and interdisciplinary research. The department offers a full range of academic programs leading to the BA, BS, MA and PhD degrees in Mathematics. In addition the department is home to the Graduate Group in Applied Mathematics which consists of faculty from the Department of Mathematics and other disciplines and which offers the MS and PhD degrees in Applied Mathematics. U. C. Davis is the third largest of the nine University of California campuses. It is conveniently located within 1-2 hours drive of the San Francisco Bay Area, the Northern California coast and the Sierra Nevada mountains. We will begin considering applications on February 15, 1994 and expect to make an offer no later than March 1, 1994. Applicants should send a curriculum vitae, a list of publications, and at least three letters of reference to: VRAP Search Committee Chair Department of Mathematics University of California Davis, California 95616-8633 It is essential that these documents contain evidence of the applicant's abilities and experience in teaching as well as research. The University of California is an equal opportunity / affirmative action employer with a strong institutional commitment to the achievement of diversity among its faculty and staff. In that spirit, we are particularly interested in receiving applications from persons of underrepresented groups including women, ethnic minorities, disabled veterans and handicapped persons. PLEASE POST ------------------------------ From: John Belward Date: Tue, 14 Dec 93 10:05:58 EST Subject: Positions at The University of Queensland POST DOCTORAL RESEARCH FELLOWSHIP AND PH.D. SCHOLARSHIPS IN AUSTRALIA Centre for Industrial and Applied Mathematics and Parallel Computing (CIAMP) High Performance Computing Unit (HPCU) DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF QUEENSLAND, AUSTRALIA. Professor Kevin Burrage and A/Professor John Belward have been awarded a 3 year ARC Collaborative Research Grant to work on the development of an integrated software environment on a supercomputer platform for land management systems in conjunction with the Queensland Department of Primary Industries. Post Doctoral applicants should have a strong background in scientific computing and have experience with vector and/or MIMD parallel programming. A working knowledge of GIS software and Database systems would also be useful. The appointment will be for a period of 3 years. Salary: \$36,285 per annum Closing date: 15 February 1994 CIAMP and the HPCU have entered into a substantial collaborative agreement with the Queensland Department of Primary Industries (QDPI) to develop and implement parallel computational algorithms with spatial modelling and environmental applications. Ph. D. Scholarships are available from CIAMP as top ups for 1994--1996 for two students with new APAs. These scholarships will each be in excess of \$5,000 for each of the three years. Applicants should have a strong background in Mathematics and Computer Science. These appointments will provide opportunity for close collaboration with a prestigious Government establishment (QDPI) on problems of national importance; access to state of the art hardware including an advanced computational lab of SUN workstations, a Silicon Graphics INDIGO, a DEC alpha workstation and colour printer; network access to a Cray YMP-2D and 4096 processor MasPar MP1 sited at the University of Queensland; a stimulating research environment of approximately 12 Ph.D students and two research fellows working on various aspects of scientific computing. Further details may be obtained from: Professor K. Burrage: phone (07) 365 3487, email address kb@maths.uq.oz.au Dr J. Belward: phone (07) 365 3257, email address jab@maths.uq.oz.au. Please forward applications and resume to the Head, Department of Mathematics, The University of Queensland, Qld 4072, fax (07)8702272. ------------------------------ From: Memphis State Date: 17 Dec 93 15:48:11 CDT Subject: Position at Memphis State To whom may be concerned. The department of Mathematical sciences of Memphis State University wants to fill a tenure track position at the assistant professor level in Probability theory. This is meant as a Mathematics position. Interested applicants should apply not later than February 1, 1994. Minorities are encouraged to apply. ------------------------------ From: Michel Cosnard Date: Mon, 13 Dec 93 09:55:46 -0500 Subject: Contents: Parallel Processing Letters Contents PARALLEL PROCESSING LETTERS Information can be obtained form the Editor in Chief, Professor Michel Cosnard at cosnard@lip.ens-lyon.fr. The content of the previous issues is available via anonymous ftp on lip.ens-lyon.fr in directory pub/LIP/users/btouranc/PPLcontents. PARALLEL PROCESSING LETTERS CONTENTS - Volume 2 - Number 4 - December 1992 Editorial Note M. Cosnard 299 Constructing An Exact Parity Base is in $RNC^{2}$ G. Galbiati, F. Maffioli 301 Parallel Constructions of Heaps and Min-Max Heaps S. Carlsson, J. Chen 311 Computation List Evaluation and Its Applications EA. Albacea 321 Data Parallel Computation of Euclidean Distance Transforms T. Bossomaier, N. Isidoro, A. Loeff 331 Two Selection Algorithms on A Mesh-Connected Computer BS. Chlebus 341 Channel Classes: A New Concept for Deadlock Avoidance in Wormhole Networks J. Duato 347 Broadcasting Time in Sparse Networks with Faulty Transmissions A. Pelc 355 A Low Overhead Schedule for A 3D-Grid Graph E. Bampis, JC Konig, D. Trystram 363 Multi-Rate Arrays and Affine Recurrence Equations PM. Lenders 373 Simulation of Genetic Algorithms on MIMD Multicomputers I. De Falco, R. Del Balio, E. Tarantino, R. Vaccaro 381 Parallel Buddy Memory Management T. Johnson, TA. Davis 391 Author Index - Volume 2 (1992) 399 ------------------------------ End of NA Digest ************************** -------