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Applied numerical linear algebra. (English) Zbl 0879.65017
Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xi, 419 p. (1997).
This is a text on linear algebra computations for beginning graduate students, written by one of the central figures in the mathematical software development in this area. The choice of material has a personal touch, and goes from the traditional, like Jacobi, Gauss Seidel and successive overrelaxation iterations for linear systems, via the standard, like the singular value decomposition (SVD), to the really sophisticated, like divide and conquer for tridiagonal eigenvalues and Jordan and Kronecker canonical forms for matrix pencils, and even into something truly exotic like Toda lattices.
The disposition is very much like a series of lectures, new concepts are introduced precisely where needed, so is SVD treated in the chapter on least squares, while the correspondence between a graph and a sparse matrix is briefly mentioned in the chapter on direct methods and in a more rigorous fashion when discussing convergence of the basic iterative methods. Illustrating examples are given, some reporting really heavy computations, but the author does not shy away from giving mathematical proofs where that is needed.
Computer implementation is everywhere the goal, and machine oriented issues like IEEE floating point arithmetic and memory hierarchies are taken into account more seriously than is common in text books at this level.

65Fxx Numerical linear algebra
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
15-04 Software, source code, etc. for problems pertaining to linear algebra