Chapter

Introduction

Jörg Liesen and Zdenek Strakos

in Krylov Subspace Methods

Published in print October 2012 | ISBN: 9780199655410
Published online January 2013 | e-ISBN: 9780191744174 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199655410.003.0001

Series: Numerical Mathematics and Scientific Computation

Introduction

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The Introduction consists of three sections that establish the general setting and give background information that is useful to know before starting to read the other chapters. In particular, it presents an overview of a typical solution process of problems in computational sciences and engineering consisting of modelling, discretisation, and computation. Here and in many other places in the book we argue that computations should always be considered in the context of the overall solution process, which is of utmost importance when computations are performed iteratively. The second section provides a brief overview of the historical evolution of topics related to the modern field of Krylov subspace methods. This also helps in putting the historical notes later in the book into their proper context. The Introduction ends with the specification of the main notation.

Keywords: solving real-world problems; modelling; discretisation; computation; errors; historical development of ideas; Krylov subspace methods; C. Lanczos; M. Hestenes; E. Stiefel

Chapter.  4102 words.  Illustrated.

Subjects: Applied Mathematics

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