*(English)*Zbl 0865.65009

[For the first edition (1983) see Zbl 0559.65011; for the second edition (1989) see Zbl 0733.65016.]

In this third edition, the authors have added to, as well as subtracted from, what there was in the previous edition, resulting in a slightly heavier (50 pages added) volume, which very well covers what is happening in this very active research area. Now, the emphasis on computations is stronger, each chapter is started with a list of the names of LAPACK routines [cf. *E. Anderson*, *Z. Bai* and *C. Bischof*, LAPACK users’ guide (1992; Zbl 0755.65028)] to call for the respective algorithms described, and reference is also given to appropriate parts of the Matlab program system. Consideration is also given to implementation issues, such as the intricacies of floating point number systems, and cache and memory hierarchies. A systematic division into subsections makes the text eminently usable as a handbook, and there is a very thorough list of references to original works, as well as to textbooks suitable for a student that meets numerical matrix computations for the first time.

##### MSC:

65Fxx | Numerical linear algebra |

65-01 | Textbooks (numerical analysis) |

65Y05 | Parallel computation (numerical methods) |

15A18 | Eigenvalues, singular values, and eigenvectors |

15A60 | Applications of functional analysis to matrix theory |