Mathematical analysis of linear/nonlinear iterative algorithms including GMRES, SOR, etc.
线性/非线性迭代算法的数学分析,包括GMRES、SOR等。
基本信息
- 批准号:09640277
- 负责人:
- 金额:$ 0.96万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:1997
- 资助国家:日本
- 起止时间:1997 至 1998
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The purpose of this research was to give mathematical foundations for linear/nonlinear iterative methods including GMRES, SOR, etc. Concerning SOR, we obtained the following results :1. Unified treatment of known convergence theorems for linear SOR methods : The Ostrowski-Reich theorem is the most famous result for convergence of the SOR method applied to the linear system Ax = b which asserts that if A is hermitian with positive diagonals, then the SOR method converges for 0 < omega < 2 if and only if A is positive definite. Some results by Householder-John, Ortega-Plemmons, etc. are also known, which are closely related to the Ostrowski-Reich theorem. We found out that. these results can uniformly be derived from the Stein theorem, which asserts that a matrix H is a convergent matrix if and only if there exists a positive definite matrix B such that BETA - H^*BH is positive definite. This simplifies and unifies the convergence proofs by Ostrowski and others.2. Global convergence of nonlinear SOR-like methods. Although Brewster-Kannan's result is known for convergence of SOR-Newton's method, it only asserts that for any initial vector there exists a sequence of parameter {omega_k}, 0< omega_k < 2 such that the process with wk at each step converges to the solution. however, the explicit choice of wk is not known. We obtained a global convergence theorem for SOR-Newton's method applied to a discretized equation for semilinear PDE, which guarantees the convergence for 0 < omega< omega^<**>_h = 2 - OMICRON(h^2) where Ii denotes the mesh size.
本研究的目的是为GMRES、SOR等线性/非线性迭代方法提供数学基础。关于SOR,我们得到以下结果:1。对已知线性SOR方法收敛性定理的统一处理:Ostrowski-Reich定理是将SOR方法应用于线性系统Ax = b的最著名的收敛性结果,该定理断言如果A是具有正对角线的厄米算子,则SOR方法在0 < < 2时收敛当且仅当A是正定的。Householder-John, Ortega-Plemmons等人的一些结果也是已知的,这些结果与Ostrowski-Reich定理密切相关。我们发现了。这些结果可以由Stein定理统一导出,该定理断言矩阵H是收敛矩阵当且仅当存在正定矩阵B使得BETA - H^*BH是正定的。这简化和统一了Ostrowski等人的收敛性证明。非线性类sor方法的全局收敛性。虽然Brewster-Kannan的结果是已知的or - newton方法的收敛性,但它只断言对于任何初始向量存在一个参数序列{omega_k}, 0< omega_k < 2,使得每一步都有wk的过程收敛到解。然而,周的明确选择是未知的。得到了半线性PDE离散方程的全局收敛定理,该定理保证了0 < omega< omega^<**>_h = 2 - OMICRON(h^2)的收敛性,其中Ii表示网格大小。
项目成果
期刊论文数量(8)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Xiaojun Chen: "On preconditioned Uzawa methods and SOR methods for saddle point problems" J.Comp.Appl.Math.100. 207-224 (1998)
陈晓军:“关于鞍点问题的预处理 Uzawa 方法和 SOR 方法”J.Comp.Appl.Math.100。
- DOI:
- 发表时间:
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- 影响因子:0
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- 通讯作者:
X.Chen: "Global and superlinear convergence of inexact Uzawa methods for saddle point problems with nondifferentiable mappings" SIAM J.Namer.Anal.35. 1130-1148 (1998)
X.Chen:“具有不可微映射的鞍点问题的不精确 Uzawa 方法的全局和超线性收敛”SIAM J.Namer.Anal.35。
- DOI:
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- 影响因子:0
- 作者:
- 通讯作者:
T.Yamamoto: "On nonlinear SOR-like methods I" Japan Journal of Industrial and Applied Math.14巻1号. 87-97 (1997)
T. Yamamoto:“关于非线性 SOR 类方法 I”《日本工业与应用数学杂志》,第 14 卷,第 1. 87-97 期(1997 年)
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
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- 通讯作者:
Xiaojun Chen: "Global and superlinear convergence of inexact Uzawa methods for saddle point problems with nondifferentiable mappings" SIAM J.Namer.Anal.35. 1130-1148 (1998)
陈晓军:“具有不可微映射鞍点问题的不精确 Uzawa 方法的全局和超线性收敛”SIAM J.Namer.Anal.35。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Xiaojun Chen: "Global and superlinear convergence of inexact Uzawa methods for saddle point problems" SIAM J.Numer.Anal.35. 1130-1148 (1998)
陈晓军:“鞍点问题的不精确 Uzawa 方法的全局和超线性收敛”SIAM J.Numer.Anal.35。
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- 影响因子:0
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YAMAMOTO Tetsuro其他文献
YAMAMOTO Tetsuro的其他文献
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{{ truncateString('YAMAMOTO Tetsuro', 18)}}的其他基金
Studies on the mechanism to gain monocyte chemotactic capacity of ribosomal protein S19 and its role in coagulum resorption.
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21590441 - 财政年份:2009
- 资助金额:
$ 0.96万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Role of plasma S19 ribosomal protein in thrombus resorption
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18590374 - 财政年份:2006
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Study on evaluation of stability of slope holding discontinuous plane causing slope failure
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15560427 - 财政年份:2003
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Analysis of CS5 co-receptor molecule that specifically inhibits chemotaxis of polymorphonuclear leukocytes
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12470058 - 财政年份:2000
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11680806 - 财政年份:1999
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Finite difference and finite element analysis for partial differential equations
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11440030 - 财政年份:1999
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S19 RIBOSOMAL PROTEIN DIMER AS MONOCYTE CHEMOTACTIC FACTOR IN CHRONIC INFLAMMATION.
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- 批准号:
08457072 - 财政年份:1996
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Studies on the membrane properties of the cat parietal cortical pyramidal neurons concerning motor compensation
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06680808 - 财政年份:1994
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Studies on The Response and Morphology of The Cortical Neurons using Double Intracellular labeling
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02670048 - 财政年份:1990
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63570167 - 财政年份:1988
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