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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.
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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.
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Convergence of iterations for linear equations.
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Softcover. VII, 177 S. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03513 3764328657 Sprache: Englisch Gewicht in Gramm: 550. Bestandsnummer des Verkäufers 2489426
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Convergence of Iterations for Linear Equations (Lectures in Mathematics. ETH Zürich)
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Convergence of Iterations for Linear Equations
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Convergence of Iterations for Linear Equations (Paperback)
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Paperback. Zustand: new. Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9783764328658
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Convergence of Iterations for Linear Equations (Lectures in Mathematics. ETH Zürich)
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Convergence of Iterations for Linear Equations (Lectures in Mathematics. ETH Zürich)
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Convergence of Iterations for Linear Equations (Lectures in Mathematics. ETH Z�rich)
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Birkh�user Basel 2008-10-10, 2008
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Convergence of Iterations for Linear Equations
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Springer, Basel, Birkhäuser Basel, Birkhäuser Jun 1993, 1993
ISBN 10: 3764328657
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 180 pp. Englisch. Bestandsnummer des Verkäufers 9783764328658
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