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Direct methods for sparse matrices. (English) Zbl 0604.65011
This is an excellent text on direct methods for solving systems of linear algebraic equations. The authors are well known for their major contributions to this subject area. They have succeeded in writing a book that contains most of the presently known algorithms. This book contains a systematic treatment of available techniques for storing, ordering and pivoting. The implementation of some specific algorithms is discussed in detail. Partitioning, matrix modification and tearing methods are explained. There is a chapter addressing the problem of sparsity outside the immediate context of solving linear equations. Relevant FORTRAN conventions and pictures of some of the sparse test matrices are given in the appendices. Reasonable number of problems in each chapter nicely complement the text. Timing data drawn from a variety of computers is presented to illustrate the various points. The book is well organized. Anyone familiar with elementary linear algebra and with some computing background will have no difficulty in appreciating the main ideas for handling sparse matrices. This book is a timely and welcome addition to the growing literature on sparse matrices.
Reviewer: R.P.Tewarson

MSC:
65F05 Direct numerical methods for linear systems and matrix inversion
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65F50 Computational methods for sparse matrices
65F30 Other matrix algorithms (MSC2010)
15-04 Software, source code, etc. for problems pertaining to linear algebra