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Titlebook: Convergence of Iterations for Linear Equations; Olavi Nevanlinna Book 1993 Springer Basel AG 1993 convergence.evolution.iteration.linear a

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發(fā)表于 2025-3-21 17:12:41 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Convergence of Iterations for Linear Equations
編輯Olavi Nevanlinna
視頻videohttp://file.papertrans.cn/238/237752/237752.mp4
叢書名稱Lectures in Mathematics. ETH Zürich
圖書封面Titlebook: Convergence of Iterations for Linear Equations;  Olavi Nevanlinna Book 1993 Springer Basel AG 1993 convergence.evolution.iteration.linear a
描述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 approxima
出版日期Book 1993
關(guān)鍵詞convergence; evolution; iteration; linear algebra; minimum; nature; operator; singularity
版次1
doihttps://doi.org/10.1007/978-3-0348-8547-8
isbn_softcover978-3-7643-2865-8
isbn_ebook978-3-0348-8547-8
copyrightSpringer Basel AG 1993
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Book 1993which 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 approxima
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On Level Sets of Quasiconformal Mappingsto establish scales of speed for the convergence of quasialgebraic operators. In order to get an initial feeling of the possible speeds, think of a self-adjoint negatively semidefinite operator . in a Hilbert space, with a countable spectrum λ. ≤ λ. ≤ … → 0. Then, if we interpolate from the left . we clearly have
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Book 1993mmetric 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 o
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發(fā)表于 2025-3-23 02:43:33 | 只看該作者
Superlinear Convergence,to establish scales of speed for the convergence of quasialgebraic operators. In order to get an initial feeling of the possible speeds, think of a self-adjoint negatively semidefinite operator . in a Hilbert space, with a countable spectrum λ. ≤ λ. ≤ … → 0. Then, if we interpolate from the left . we clearly have
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A System for Video Object Segmentation, norms. Unless explicitly stated otherwise, continuity, convergence etc. is to be understood in terms of the norm topology in . and in the uniform operator topology for operators. Our main goal to start with is to estimate powers of . in the form ..
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