Convergence of Iterations for Linear Equations

By:

Olavi Nevanlinna

Format:

Paperback / softback

Series:

Lectures in Mathematics. Eth Zurich

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Description

Discussing the convergence of Krylov subspace methods for solving fixed point problems, this work focuses on the dynamical aspects of the iteration processes. For example, there are many similarities between the evolution of a Krylov subspace process and that of linear operator semigroups, in particular in the beginning of the iteration. A lifespan of an interation might typically start with a fast but slowing phase. Such a behaviour is sublinear in nature, and is essentially independent of whether the problem is singular or not. Then, for nonsingular problems, the iteration might run with a linear speed before a possible superlinear phase. All these phases are based on differential mathematical mechanisms which the book outlines. Its aim is to understand how to precondition effectively, both in the case of "numerical linear algebra" (where one usually thinks of first fixing a finite dimensional problem to be solved) and in function spaces where the "preconditioning" corresponds to software which approximately solves the original problem.

Release date Australia

March 31st, 1993

Author

Olavi Nevanlinna

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational

Illustrations

15 Illustrations, black and white; VIII, 180 p. 15 illus.

Pages

180

Series

Lectures in Mathematics. Eth Zurich

Dimensions

170x244x10

ISBN-13

9783764328658

Product ID

3070558

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