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

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。
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    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。
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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:
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  • 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 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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    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.
核糖体蛋白S19获得单核细胞趋化能力的机制及其在凝血吸收中的作用研究。
  • 批准号:
    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
血浆S19核糖体蛋白在血栓吸收中的作用
  • 批准号:
    18590374
  • 财政年份:
    2006
  • 资助金额:
    $ 0.96万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Study on evaluation of stability of slope holding discontinuous plane causing slope failure
导致边坡失稳的边坡稳定性评价研究
  • 批准号:
    15560427
  • 财政年份:
    2003
  • 资助金额:
    $ 0.96万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Analysis of CS5 co-receptor molecule that specifically inhibits chemotaxis of polymorphonuclear leukocytes
特异性抑制多形核白细胞趋化性的CS5共受体分子分析
  • 批准号:
    12470058
  • 财政年份:
    2000
  • 资助金额:
    $ 0.96万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
ELECTROPHY SIOLOGICAL AND MORHPHOLOGICAL STUDIES ON INTERACTION BETWEEN THE CEREBELLAR AND BASAL GANGLIA INPUTS.-ANALYSIS OF INTEGRATION IN THE CEREBRAL CORTEX-
关于小脑和基底神经节输入之间相互作用的电学和形态学研究。-大脑皮层整合分析-
  • 批准号:
    11680806
  • 财政年份:
    1999
  • 资助金额:
    $ 0.96万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Finite difference and finite element analysis for partial differential equations
偏微分方程的有限差分和有限元分析
  • 批准号:
    11440030
  • 财政年份:
    1999
  • 资助金额:
    $ 0.96万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
S19 RIBOSOMAL PROTEIN DIMER AS MONOCYTE CHEMOTACTIC FACTOR IN CHRONIC INFLAMMATION.
S19 核糖体蛋白二聚体作为慢性炎症中的单核细胞趋化因子。
  • 批准号:
    08457072
  • 财政年份:
    1996
  • 资助金额:
    $ 0.96万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Studies on the membrane properties of the cat parietal cortical pyramidal neurons concerning motor compensation
猫顶叶皮层锥体神经元运动补偿膜特性的研究
  • 批准号:
    06680808
  • 财政年份:
    1994
  • 资助金额:
    $ 0.96万
  • 项目类别:
    Grant-in-Aid for General Scientific Research (C)
Studies on The Response and Morphology of The Cortical Neurons using Double Intracellular labeling
双细胞内标记研究皮质神经元的反应和形态
  • 批准号:
    02670048
  • 财政年份:
    1990
  • 资助金额:
    $ 0.96万
  • 项目类别:
    Grant-in-Aid for General Scientific Research (C)
ROLE OF HAGEMAN FACTOR-KALLIKREIN-KININ SYSTEM IN HOST DEFENCE AGAINST BACTERIAL INFECTIONS.
哈格曼因子-激肽释放酶-激肽系统在宿主防御细菌感染中的作用。
  • 批准号:
    63570167
  • 财政年份:
    1988
  • 资助金额:
    $ 0.96万
  • 项目类别:
    Grant-in-Aid for General Scientific Research (C)
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