Direct methods for sparse linear systems.

*(English)*Zbl 1119.65021
Fundamentals of Algorithms 2. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-13-9/pbk; 978-0-89871-888-1/ebook). xii, 217. (2006).

Fundamentals of sparse matrix algorithms for the direct solution of sparse linear systems are presented in this book. The author’s goal is to present algorithms that are fast, require low storage, are concise, easy to understand and short, cover a wide variety of matrix operations, and are accurate and robust. Knowledge of pseudo-code, MATLAB and C is assumed. Furthermore, a basic knowledge of linear algebra, graph theory, algorithms, and data structures is assumed.

In the introductory chapter, a brief review of these topics is given. The next three chapters are on basic algorithms, solving triangular systems and Cholesky factorization. Orthogonal methods, LU factorization and fill-reducing orderings are treated in the following chapters. The last three chapters are on solving sparse linear systems, CSparse (a stand alone sparse matrix package) and sparse matrices in MATLAB. An appendix is given on the basics of the C programming language. Some citations appear in the body of each chapter and are discussed at the end.

The author has done an excellent job of collecting a large amount of information and presenting it in a concise and clear manner. This book is a welcome addition to the vast literature on sparse matrices.

In the introductory chapter, a brief review of these topics is given. The next three chapters are on basic algorithms, solving triangular systems and Cholesky factorization. Orthogonal methods, LU factorization and fill-reducing orderings are treated in the following chapters. The last three chapters are on solving sparse linear systems, CSparse (a stand alone sparse matrix package) and sparse matrices in MATLAB. An appendix is given on the basics of the C programming language. Some citations appear in the body of each chapter and are discussed at the end.

The author has done an excellent job of collecting a large amount of information and presenting it in a concise and clear manner. This book is a welcome addition to the vast literature on sparse matrices.

Reviewer: R. P. Tewarson (Stony Brook)

##### MSC:

65F05 | Direct numerical methods for linear systems and matrix inversion |

65F50 | Computational methods for sparse matrices |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |