Matrix iterative analysis. 2nd revised and expanded ed. (English) Zbl 0998.65505

Springer Series in Computational Mathematics. 27. Berlin: Springer. x, 358 p. (2000).
Publisher’s description: This book is a revised version of the first edition, originally published by Prentice Hall in 1962 and regarded as a classic in its field. In some places, newer research results, e.g. results on weak regular splittings, have been incorported in the revision, and in other places, new material has been added in the chapters, as well as at the end of chapters, in the form of additional up-to-date references and some recent theorems to give the reader some newer directions to pursue. The material in the new chapters is basically self-contained and more exercises have been provided for the readers. While the original version was more linear algebra oriented, the revision attempts to emphasize tools from other areas, such as approximation theory and conformal mapping theory, to access newer results of interest. The book should be of great interest to researchers and graduate students in the field of numerical analysis.


65F10 Iterative numerical methods for linear systems
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15B48 Positive matrices and their generalizations; cones of matrices
15A06 Linear equations (linear algebraic aspects)
41A21 Padé approximation
41A10 Approximation by polynomials
39A10 Additive difference equations


Zbl 0133.08602