Item description for Matrix Iterative Analysis (Springer Series in Computational Mathematics) by Richard S. Varga...
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.
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Est. Packaging Dimensions: Length: 9.4" Width: 6.35" Height: 0.92" Weight: 1.28 lbs.
Release Date Apr 26, 2000
ISBN 3540663215 ISBN13 9783540663218
Availability 107 units. Availability accurate as of Oct 25, 2016 01:15.
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Reviews - What do customers think about Matrix Iterative Analysis (Springer Series in Computational Mathematics)?
Excellent, but very dated Jun 3, 2001
The Editorial Review on this site's site says: "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". These remarks give an incorrect flavor for the book. Of approximately 350 references, less than a dozen are post 1990. The vast majority are from 1950 to 1965. The author repeatedly refers to "more recent" results with references to the early 1960's. So much for "newer results". The author's remarks in the preface to the new edition are much more informative: "...just what could easily be added [to the new edition]. For example, even a modest treatment of finite elements...was questionable. This was also the case for multigrid methods, Krylov subspace methods, preconditioning methods, and incomplete factorization methods. In the end, only a few items were added... These items include ovals of Cassini, a semi-iterative analysis of SOR methods,.... and matrix rational approximations to exp(-z)."
You will notice that "conformal mapping" didn't make the grade as a centerpiece of the new edition, and neither is it mentioned in the Table of Contents, nor the Index.
For what is here, the exposition is clear and helpful. However, the reader won't gain much perspective on new developments.