Numerical methods in matrix computations. (English) Zbl 1322.65047

Björck, Åke

Texts in Applied Mathematics 59. Cham: Springer (ISBN 978-3-319-05088-1/hbk; 978-3-319-05089-8/ebook). xvi, 800 p. (2015).

The book is really an excellent reference on matrix algorithms that are at the core of scientific computing and are an indispensable tool in most applications in engineering. The author is a professor emeritus at the Department of Mathematics, Linköping University and a Fellow of the Society of Industrial and Applied Mathematics.
The book gives a comprehensible and up-to-date treatment of methods and algorithms in matrix computations. Both direct and iterative methods for linear systems and eigenvalue problems are covered. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given.
The book is suitable for use in courses in scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book very useful also as a reference and guide to further study and research work.

Reviewer: Sonia Pérez Díaz (Madrid)

MSC:

65Fxx	Numerical linear algebra
65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65F05	Direct numerical methods for linear systems and matrix inversion
65F15	Numerical computation of eigenvalues and eigenvectors of matrices
65F10	Iterative numerical methods for linear systems
65F20	Numerical solutions to overdetermined systems, pseudoinverses

Keywords:

direct methods; matrix computations; linear systems; linear least squares; matrix eigenvalues; iterative methods; textbook