##
**Matrix computations.
3rd ed.**
*(English)*
Zbl 0865.65009

Baltimore, MD: The Johns Hopkins Univ. Press. xxvii, 694 p. (1996).

[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.

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.

Reviewer: A.Ruhe (Göteborg)

### MathOverflow Questions:

efficient numerical algorithm for matrix determinantHow can I calculate eigenvalues of a tridiagonal matrix?

### MSC:

65Fxx | Numerical linear algebra |

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

65Y05 | Parallel numerical computation |

15A18 | Eigenvalues, singular values, and eigenvectors |

15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |

### Keywords:

matrix computations; matrix algebra; Gaussian elimination; orthogonalization; least squares methods; eigenvalue problem; Lanczos methods; iterative methods; functions of matrices; matrix multiplication; parallel matrix computation; MATLAB; LAPACK routines
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\textit{G. Golub} and \textit{C. F. Van Loan}, Matrix computations. 3rd ed. Baltimore, MD: The Johns Hopkins Univ. Press (1996; Zbl 0865.65009)

### Digital Library of Mathematical Functions:

§3.2(ii) Gaussian Elimination for a Tridiagonal Matrix ‣ §3.2 Linear Algebra ‣ Areas ‣ Chapter 3 Numerical Methods§3.2(i) Gaussian Elimination ‣ §3.2 Linear Algebra ‣ Areas ‣ Chapter 3 Numerical Methods

Example ‣ §3.2(i) Gaussian Elimination ‣ §3.2 Linear Algebra ‣ Areas ‣ Chapter 3 Numerical Methods

§3.2(vii) Computation of Eigenvalues ‣ §3.2 Linear Algebra ‣ Areas ‣ Chapter 3 Numerical Methods