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**Computer solution of large linear systems.**
*(English)*
Zbl 0934.65032

Studies in Mathematics and its Applications. 28. Amsterdam: Elsevier. 776 p. (1999).

The monograph gives an excellent overview over the state-of-the-art algorithms for the solution of large linear systems as they typically arise from the discretization of partial differential equations. The book contains 10 chapters. Chapter 1 provides the mathematical background that is necessary for understanding and studding the solution methods for linear systems. The next 3 chapters are devoted to direct methods, namely Gaussian elimination for general and sparse systems, special variants, and fast direct solvers. In Chapter 5, the author provides an overview over the classical iterative methods. Chapters 6 deals with the conjugate gradient method and related methods for symmetric and positive definite systems. Chapter 7 is devoted to Krylov methods for non-symmetric systems. Different preconditioning techniques are described in Chapter 8. Finally, the multigrid methods and the domain decomposition techniques are presented in Chapters 9 and 10, respectively. The monograph will certainly become the standard book for linear system solvers.

Reviewer: U.Langer (Linz)

### MSC:

65F10 | Iterative numerical methods for linear systems |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

65F35 | Numerical computation of matrix norms, conditioning, scaling |

65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |

65F05 | Direct numerical methods for linear systems and matrix inversion |

65F50 | Computational methods for sparse matrices |