Back MatterSource: SIAM Review, Vol. 24, No. 4 (Oct., 1982)Published by: Society for Industrial and Applied MathematicsStable URL: http://www.jstor.org/stable/2029568 .

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LINPACK USERS' GUIDE J. J. Dongarra, J. R. Bunch, C. B. Moler and G. W Stewart

The authors of this carefully structured guide LINPACK is designed to be machine-inde- are the principal developers of LINPACK, a pendent and fully portable. There are no unique package of Fortran subroutines for machine-dependent constants because there is analyzing and solving various systems of simul- little need to check for "small" numbers. There taneous linear algebraic equations and linear is no mixed-precision arithmetic. There are no least squares problems. input/output statements, no character LINPACK is designed to execute at near op- manipulations, and no COMMON or EQUIVA- timum efficiency in most operating environ- LENCE statements. ments. The algorithms employed are the most LINPACK's column orientation requires revision reliable and accurate known. Newly developed of some conventional algorithms, but results in algorithms help estimate the accuracy of the significant improvement in performance on computed results. The package's subroutines operating systems with paging and cache capitalize on various special properties of memory. matrices to save computer time and storage. Contents: Preface * Introduction * General LINPACK's division of labor (most linear equa- matrices * Band matrices * Positive definite tion problems will require two LINPACK matrices * Positive definite band matrices 9 subroutines, one to process the coefficient Symmetric indefinite matrices * Triangular matrix and one to process a particular right- matrices * Tridiagonal matrices * The Cholesky hand side) results in significant savings of com- decomposition * The QR decomposition * Up- puter time. dating QR and Cholesky decompositions * The LINPACK handles full matrices of order up to a singular value decomposition * References * few hundred and band matrices of order up to Appendix A: Basic linear algebra subprograms* several thousand. Appendix B: Timing data * Appendix C: Program Variants of all the subroutines are provided for listings * Appendix D: BLA listings single-precision, double-precision, complex9,toswh viii + 367 pp. and double-precision complex arithmetic. $17.00/list, $13.60/SIAM member

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METHODS AND APPLICATIONS OF I NTERVAL ANALYSIS by Ramon E. Moore

"An exciting new book by Ramon E. Moore, tools with direct applicability to important prob- coupled with fast-paced modern technological lems in scientific computing. This major work advances, may herald the coming-of-age of a will bring you up-to-date on many remarkable surefire technique for dealing with the bother- elements in the field which have appeared dur- some error inherent in many computational pro- ing the last decade; and it serves as a guide to cedures .i.p. Indeed, it seems that the range of the current literature. applications of interval mathematics is limited A special feature is the inclusion of the only by the imagination of the scientific com- bibliographyton interval methods compiled by K. munity."-J. Michael Yohe in SIAM News, Feb., Nickel, F. Bierbaum, and K. P. Schwierz. 1980. ~ ~~~~~~~~~~~~~Contents: Introduction * Finite representations * Finite evalua-

This is the first book in ten years on an increas- tion * Finite convergence * Computable sufficient conditions for ingly important set of techniques that provide a existence and convergence * Safe starting regions for iterative

mathematically rigorous and complete error, methods * Applications to mathematical programming ., Ap- plications to operator equations * An application in finance: In- analysis for computational results. It shows ternal rates-of-return

that interval analysis provides a powerful set of 1979, xi + 190 pp. $16.00/list, $12.80/SIAM member

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probab'~~~~An1973, v + FUNCION ~~~~~ ~~~~~~~~ 64~~~~~)porlgPp., $6011s$. 20sA

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~ Membr pric also pplies toicnlreelafiaatdoranzainsofreS For further information,ewrite to SocietyforIndStra and Apled Mathemsaticst .. 11 Sot 7hStet*Piadlpia P 110

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Fourier Analysis =0 X 8h of NumnericalAA

Approximations of L 2 Hyperbolic Equations 1- = C by R.Vichnevetsky and, J. B. Bowles v V x A monograph for those concerned with computational fluid dynamics; for physicists and engineers who work with computers in the analysis of problems in hydraulics, gas dynamics, plasma physics, numerical weather prediction, and transport processes in engineering; for applied mathematicians concerned with the more theoretical aspects of these computations; and for students.

CONTENTS: Introduction * Fourier Analysis of the Accuracy of Semi- Discretizations * Higher Order Semi-Discretizations * Full DiscretizationsO Damping, Diffusion and Filtering * Group Velocity * Time-Fourier Transforms * Fourier Analysis and L2-Norm of the Global Error * Spectral Methods * Equations in Two Dimensions: Anisotropy * Bibliography * Index

xii + 135 pp, hardcover. $21.50/list, $17.20/SIAM member

Send order to: SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS i5 i rn P.O. Box 7260e Philadelphia, PA 19101

INVERSE SCATIERING PAPERS: 1955-1963 by 1. Kay and H. E. Moses, $30.00

This book is a collection of classical papers on inverse scattering. Among the topics are the general Gel'fand-Levitan equation, inverse problems for transmission line equations, and propagation of electromagnetic radiation and sound through stratified media. The one-dimensional problem and the reflectionless potentials, as treated in the papers, form the basis of the inverse scattering transform as applied to non-linear equations and the theory of solitons.

ALSO OF INTEREST

CARTANIAN GEOMETRY, NON-LINEAR WAVES AND CONTROL THEORY, PARTS A AND B by R. Hermann $60.00 per part.

QUANTUM STATISTICAL MECHANICS AND LIE GROUP HARMONIC ANALYSIS by N. Hurt and R. Hermann $33.00.

DEVELOPMENT OF MATHEMATICS IN THE 19TH CENTURY by Felix Klein (translated by M. Ackerman) $60.00.

From MATH SCI PRESS 53 Jordan Road, Brookline, MA 02146 * Phone: (617) 738-0307

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SOLITO NS~~~~~0 FRONT REAR

ANDTE 04-

by M. J. Ablowitz -12 and H. Segur

Here is a complete exposition of the inverse scattering transform and its application to problems of nonlinear dispersive waves. The theory provides a rich spectrum of new ideas in mathematics with interesting results in differential geometry, analytic function theory, algebraic geometry, partial and ordinary differential equations, difference equations, and integral equations.

This book contains a broad selection of material relating to what is commonly called "soliton theory"; it serves not only as an introduction and foundation for studying the inverse scattering transform, but also as a treatise on the subject. It introduces the reader to solitons and the inverse scattering transform, brings the reader to the forefront of current research, and simultaneously provides a suitable text for graduate students.

Ablowitz and Segur have been working in the area of nonlinear waves and soliton theory for almost fifteen years. Collectively, they have written more than 75 research papers, a number of which are considered to be seminal papers in the field They have been principal lecturers at numerous national and international conferences. Mark Ablowitz received his Ph.D. in mathematics from Massachusetts Institute of Technology in 1971. He is currently chairman of the mathematics department of Clarkson College. Harvey Segur received his Ph.D. in mechanical engineering from the University of California at Berkeley. He joined the mathematics department at Clarkson College in 1971, after a postdoctoral appointment in applied mathematics at California Institute of Technology. He is senior consultant at Aeronautical Research Associates of Princeton.

$54.50 list, $43.60 SIAM member 1981, 440 pages

Save postage and handling charges by including payment with order.

For further information write to or phone:

Society for Industrial and Applied Mathematics 117 South 17th Street Philadelphia, PA 19103 215 564 2929

1 slIan - -

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OCTOBER * 1982 VOLUME 24 NUMBER 4

A PUBLICATION OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS

CONTENTS

ARTICLES Perturbation Expansions on Perturbed Domains ................................. N. R. Lebovitz 381 Time-Dependent Queues .................................................. Joseph B. Keller 401 The Significance of the Stability of Difference Schemes in Different lP-Spaces . ........... T Geveci 413 Understanding the QR Algorithm .......................................... David S. Watkins 427 On the Existence of Positive Solutions of Semilinear Elliptic Equations ................. P. L. Lions 441 Optimal Mapping from a Sphere onto a Plane .......... ....................... Carl E. Pearson 469

PROBLEMS Malevolent Traffic Lights ................................................... J. C. Lagarias 477 A Definite Integral ...................................................... Peter Henrici 477 "Bad" Triangles in Hilbert Space ............................................... M. Burnashev 477 A Binomial Coefficient Summation ................ .......................... Gengzhe Chang 478 Asymptotic Behavior of an n-fold Integral .............. A. M. Odlyzko, L. A. Shepp and D. Slepian 478

SOLUTIONS A Functional Equation (K. R. Parthasarathy) .................................... B. R. Ebanks 478 Power Series of an Elliptic Function (M. L. Glasser) ............................. W. B. Jordan 479 A Learning Model (Y. P. Sabharwal and B. R. Gupta) .............................. P. Guttorp 479 A Nonlinear Second Order Differential Equation (E. Y. Rodin) ......... H. E. Fettis and G. Wanner 480 Inequality or Identity (E. A. van Doorn) ....................................... Otto G. Ruehr 481

BOOK REVIEWS Self-Organization in Nonequilibrium Systems (G. Nicolis and I. Prigogine) ......... Hans G. Othmer 483 Sturmian Theory for Ordinary Differential Equations (William T. Reid) ................ Alan Lazer 485 Sequence Transformations and Their Applications (Jet Wimp) ...................... Yudell L. Luke 489 Spline Functions (Larry Schumaker) ........................................... J. H. Ahlberg 490 Mathematical Population Genetics (Warren J. Ewens) ........................... Stanley Sawyer 491 Approximation Theory and Methods (M. J. D. Powell) ......................... Charles K. Chui 493 A History of the Calculus of Variations from the 17th Through the 19th Century (Herman H. Goldstine)

Hans Sagan 494 Spectral Theory of Ordinary Differential Operators (Erich Muller-Pfeiffer) ........ Martin Schechter 495 Free Oscillations of the Earth (E. R. Lapwood and T. Usami) .................. Susan Friedlander 496 Catastrophe Theory and Bifurcations: Applications to Urban and Regional Systems (A. G. Wilson)

N. D. Kazarinoff 497 Theory and Applications of Hopf Bifurcation (D. D. Hassard, N. D. Kazarinoff and Y-H Wan)

Kenneth R. Meyer 498 Linear Algebra and Its Applications (Gilbert Strang) . .................. Nicholas J. Rose 499 Perturbation Methods in Applied Mathematics (J. Kevorkian and J. D. Cole) .......... R. E. Meyer 501 Axiomatic Models of Bargaining (Alvin E. Roth) . .................... Martin Shubik 501

CHRONICLE Articles Appearing in Currenf and Future Issues of other SIAM Journals .505 New Members .511 Treasurer's Report .515

CODEN: SIREAD

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