Iterative Krylov Methods for Large Linear Systems (Cambridge Monographs on Applied and Computational Mathematics Book 13) 1st Edition by Henk A. van der Vorst (PDF)

Description

Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book was extremely helpful and relatively readable. Be prepared to work hard to get the best of the information in it, however. This is definitely a graduate text in Mathematics and as such assumes a high level of previous knowledge. Since I know Linear Algebra at a basic level but was new to this field, it was necessary to look up some things in Wikipedia or other sources. There are some cases where the author leaves large gaps that require you to use Algebra and various definitions to follow along with his reasoning. He simply say “and we can see” or some such and expect that you figure it out. So that’s why only 4 stars. Overall though, the information contained in this book was exactly what I wanted and I now have a much better understanding of solving large Linear Systems with the iterative methods he goes into.

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