And Descriptions of Tables and Books

This book is more than a guide for users of LINPACK subroutines. LINPACK is a package of well-structured, portable, Fortran subroutines that solve linear systems of equations and some related problems. The related problems include ordinary leastsquares, inverses, determinants, and the condition estimator for the solution of linear systems of equations. The software, and thus this guide for users, addresses computations for dense matrices. The preface presents the background and the goals of LINPACK, a three-year project sponsored jointly by the National Science Foundation and the Department of Energy. The introduction gives an overview of the linear systems problems in LINPACK, the structure of the subroutines, the naming conventions and the software design. General numerical properties having to do with rounding errors, accuracy of computed results, and detection of singularity are discussed. The introduction contains an especially good discussion on the need and strategies for scaling; a section that should be studied by originators of linear systems problems. The book contains eleven chapters, references, and four appendices. Each chapter addresses a particular decomposition, and most of the chapters contain background numerical information, algorithmic details, directions for use of the subroutines, and programming and performance details. LINPACK includes subroutines for LU decomposition, QR orthogonal factorizations by Householder transformations, Cholesky decomposition, and the singular value decomposition. Matrices of special structure are treated separately and include positive definite symmetric, symmetric indefinite, positive definite band, triangular, and tridiagonal matrices. A separate chapter treats updating QR and Cholesky decompositions. The notation used in the chapters on QR and the singular value decompositions is taken from the statistical model, y = Xß + e. The notation in other chapters follows that of standard numerical linear algebra, ,4x = b. The four appendices include the Basic Linear Algebra Subprograms, timing data, program listings for the real single precision subroutines in LINPACK, and the BLA listings. LINPACK, itself, contains single and double precision real and complex versions of the software, which can be obtained on tape from the National Energy Software Center or from International Mathematical and Statistical Libraries, Inc. The subroutines in LINPACK are well-documented. The LINPACK User's Guide will be useful to the naive or sophisticated user of LINPACK. Furthermore, the book will be extremely useful to teachers and students of linear algebra. Students in computer