Matrix Iterative Analysis (Springer Series in Computational Mathematics)

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This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.

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Matrix Iterative Analysis (Springer Series in Computational Mathematics) Review

The Editorial Review on Amazon'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. Help other customers find the most helpful reviews Was this review helpful to you?�Yes No Report abuse | PermalinkComment Comment

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