Iterative solution of large sparse systems of equations. Transl. from the German.

*(English)*Zbl 0789.65017
Applied Mathematical Sciences. 95. New York, NY: Springer-Verlag. xxi, 429 p. (1994).

The present book is a translation of the German original [Iterative Lösung großer schwachbesetzter Gleichungssysteme (1991; Zbl 0729.65018)] and can be viewed as both textbook and monograph. The book is devoted exclusively to iterative methods for the solution of systems of linear algebraic equations, first of all to (large sparse) systems arising from discretization of partial differential equations. The author, well-known from his great contribution to the development of modern iterative methods, gives here excellent very systematic review of various iterative techniques starting from the classical ones and continuing to very recent methods. The explanation is very proportional and reflects all the important features of the present state of the art.

The book will be useful to all who are interested in application and theory of the iterative methods. Besides the description and analysis of various iterative techniques great attention is devoted also to questions of computational work, efficiency and computer implementation. The book includes many procedures written in Pascal which can be also requested on disk from the author. The book originates from university lectures and can be very successfully exploited for teaching purposes.

Concise content: General questions concerning iterative methods; classical iterative methods in the cases of positive definite matrices, 2-cyclic matrices and \(M\)-matrices; semi-iterative methods; transformations; preconditioning; incomplete triangular decompositions; conjugate gradient methods; multigrid methods; domain decomposition methods.

The book will be useful to all who are interested in application and theory of the iterative methods. Besides the description and analysis of various iterative techniques great attention is devoted also to questions of computational work, efficiency and computer implementation. The book includes many procedures written in Pascal which can be also requested on disk from the author. The book originates from university lectures and can be very successfully exploited for teaching purposes.

Concise content: General questions concerning iterative methods; classical iterative methods in the cases of positive definite matrices, 2-cyclic matrices and \(M\)-matrices; semi-iterative methods; transformations; preconditioning; incomplete triangular decompositions; conjugate gradient methods; multigrid methods; domain decomposition methods.

Reviewer: R.Blaheta (Ostrava)

##### MSC:

65F10 | Iterative numerical methods for linear systems |

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

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

35J25 | Boundary value problems for second-order elliptic equations |

65F50 | Computational methods for sparse matrices |

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