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Iterative methods for solving linear systems. (English) Zbl 0883.65022
Frontiers in Applied Mathematics. 17. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xiv, 220 p. (1997).
This is an excellent book on iterative methods for solving linear equations. After an overview on the state of the art, the author develops a theory that explains the effects of rounding errors on the convergence rate of the conjugate gradients method. All relevant new methods also for non-symmetric systems are presented: Orthomin, Orthodir, Minres, Gmres, BiCG and related methods. The second part of the book deals with preconditioners and model problems for solving partial differential equations. Besides the classical preconditioners Gauss-Seidel, successive overrelaxation and incomplete Cholesky also multigrid and domain decomposition methods are discussed.
Reviewer: W.Gander (Zürich)

65F10 Iterative numerical methods for linear systems
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65F35 Numerical computation of matrix norms, conditioning, scaling
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65G50 Roundoff error