9780198739043-0198739044-Krylov Subspace Methods: Principles and Analysis (Numerical Mathematics & Scientific Computation) (Numerical Mathematics and Scientific Computation)

Krylov Subspace Methods: Principles and Analysis (Numerical Mathematics & Scientific Computation) (Numerical Mathematics and Scientific Computation)

ISBN-13: 9780198739043
ISBN-10: 0198739044
Edition: Reprint
Author: Liesen, Jorg, Strakos, Zdenek
Publication date: 2015
Publisher: Oxford University Press
Format: Paperback 408 pages
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Book details

ISBN-13: 9780198739043
ISBN-10: 0198739044
Edition: Reprint
Author: Liesen, Jorg, Strakos, Zdenek
Publication date: 2015
Publisher: Oxford University Press
Format: Paperback 408 pages

Summary

Acknowledged authors Liesen, Jorg, Strakos, Zdenek wrote Krylov Subspace Methods: Principles and Analysis (Numerical Mathematics & Scientific Computation) (Numerical Mathematics and Scientific Computation) comprising 408 pages back in 2015. Textbook and eTextbook are published under ISBN 0198739044 and 9780198739043. Since then Krylov Subspace Methods: Principles and Analysis (Numerical Mathematics & Scientific Computation) (Numerical Mathematics and Scientific Computation) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments, and therefore Krylov subspace methods can be viewed as matching moments model reduction. This allows enlightening reformulations of questions from matrix computations into the language of orthogonal polynomials, Gauss-Christoffel quadrature, continued fractions, and, more generally, of Vorobyev's method of moments. Using the concept of cyclic invariant subspaces, conditions are studied that allow the generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the important practical distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. The investigation includes effects of finite precision arithmetic and focuses on the method of conjugate gradients (CG) and generalised minimal residuals (GMRES) as major examples.

There is an emphasis on the way algebraic computations must always be considered in the context of solving real-world problems, where the mathematical modelling, discretisation and computation cannot be separated from each other. The book also underlines the importance of the historical context and demonstrates that knowledge of early developments can play an important role in understanding and resolving very recent computational problems. Many extensive historical notes are included as an inherent part of the text as well as the formulation of some omitted issues and challenges which need to be addressed in future work.

This book is applicable to a wide variety of graduate courses on Krylov subspace methods and related subjects, as well as benefiting those interested in the history of mathematics.

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