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Based on extensive research by Henk van der Vorst, this book presents an overview of a number of Krylov projection methods for the solution of linear systems of equations. Van der Vorst demonstrates how these methods can be derived from basic iteration formulas and how they are related. Focusing on the ideas behind the methods rather than a complete presentation of the theory, the volume includes a substantial amount of references for further reading as well as exercises to help students initially encountering the material.

The idea for this book originated during the workshop "Model order reduction, coupled problems and optimization" held at the Lorentz Center in Leiden from S- tember 19-23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers,...