Convergence of Iterations for Linear Equations (Lectures in Mathematics. ETH Zürich) - Softcover

Nevanlinna, Olavi

 
9783764328658: Convergence of Iterations for Linear Equations (Lectures in Mathematics. ETH Zürich)
Softcover
ISBN 10: 3764328657 ISBN 13: 9783764328658
Verlag: Birkhäuser Basel, 2008

Inhaltsangabe

Assume that after preconditioning we are given a fixed point problem x = Lx + f (*) where L is a bounded linear operator which is not assumed to be symmetric and f is a given vector. The book discusses the convergence of Krylov subspace methods for solving fixed point problems (*), and 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 iteration might typically start with a fast but slowing phase. Such a behavior 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 different mathematical mechanisms which the book outlines. The goal is to know 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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

Assume that after preconditioning we are given a fixed point problem x = Lx + f (*) where L is a bounded linear operator which is not assumed to be symmetric and f is a given vector. The book discusses the convergence of Krylov subspace methods for solving fixed point problems (*), and 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 iteration might typically start with a fast but slowing phase. Such a behavior 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 different mathematical mechanisms which the book outlines. The goal is to know 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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Birkhäuser Basel
Erscheinungsdatum
2008
Sprache
Englisch
ISBN 10 
3764328657
ISBN 13 
9783764328658
Einband
Tapa blanda
Anzahl der Seiten
192
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

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9780817628659: Convergence of Iterations for Linear Equations (Lectures in Mathematics Eth Zurich)

Vorgestellte Ausgabe

ISBN 10:  0817628657 ISBN 13:  9780817628659
Softcover