共查询到20条相似文献,搜索用时 15 毫秒
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白中治 《高等学校计算数学学报》1997,19(1):28-39
1 引言 众所周知,许多微分方程经过差分或有限元离散,即可归结为线性代数方程组 Ax=b,A∈L(R~n)非奇异,x,b∈R~n.(1.1)缘于原问题的物理特性,系数矩阵A∈L(R~n)通常是大型稀疏的,并且具有规则的分块结构。鉴此,文[1]基于矩阵多重分裂的概念,并运用线性迭代法的松弛加速技巧,提出了求解这类大型稀疏分块线性代数方程组的并行矩阵多分裂块松弛迭代算法,并在适当的条件下建立了算法的收敛理论。对于SIMD多处理机系统,这类算法是颇为适用和行之有效的。 相似文献
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ONMONOTONECONVERGENCEOFNONLINEARMULTISPLITTINGRELAXATIONMETHODS¥WANGDEREN;BAIZHONGZHI(DepazatmentofMathematics,ShsllghaiUnive... 相似文献
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Zhong-zhi Bai 《计算数学(英文版)》1998,(3)
1.IntroductionMultisplittingmethodsforgettingthesolutionoflargesparsesystemoflinearequationsAx=b,A=(and)6L(Rn)nonsingular,x=(x.),b=(b.)eR"(1.1)areefficientparalleliterativemethodswhicharebasedonseveralsplittingsofthecoefficientmatrixAEL(R").Following[11th… 相似文献
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白中治 《高校应用数学学报(A辑)》1995,(2):133-140
在本文中,我们设计了求解大型线性代数方程组的适用于MIMD系统的异步并行多分裂松弛算法的一般模型,并在系数矩阵是H-矩阵的条件下,建立了该一般模型的收敛性理论。 相似文献
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ON THE CONVERGENCE OF ASYNCHRONOUS NESTED MATRIX MULTISPLITTING METHODS FOR LINEAR SYSTEMS 总被引:1,自引:0,他引:1
Zhong-zhi Bai 《计算数学(英文版)》1999,(6)
1.IntroductionTherehasbeenalotofliterature(see[1]--[61and[12])ontheparalleliterativemethodsforthelarge--scalesystemoflinearequationsinthesenseofmatrixmultisplittingsincethepioneeringworkofO'LearyandWhite(see[l])waspublishedin1985.Oneofthemostrecentre... 相似文献
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Zhong-zhi Bai 《计算数学(英文版)》1998,(6)
1.IntroductionTheclassicaliterativemethods,suchastheJacobimethod,theGauss-SeidelmethodandtheSORmethod,aswellastheirsymmetrizedvariants,playanimportantroleforsolvingthelargesparsesystemoflinearequationsInaccordancewiththebasicextrapolationprincipleofthelineariterativemethod,Hadjidimos[1]furtherproposedaclassofacceleratedoverrelaxation(AOR)methodforsolyingthelinearsystem(1.1)in1978.Thismethodincludestwoarbitraryparameters,andtheirsuitablechoicesnotonlycannaturallyrecovertheJacobi,theGauss-S… 相似文献
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Jian-yuPan Zhong-zhiBai 《计算数学(英文版)》2004,22(5):681-698
We study a class of blockwise waveform relaxation methods,and investigate its con-vergence properties in both asymptotic and monotone senses.In addition,the monotoneconvergence rates between different pointwise/blockwise waveform relaxation methods re-sulted from different matrix splittings,and those between the pointwise and blockwisewaveform relaxation methods are discussed in depth. 相似文献
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Zhong-zhi Bai 《计算数学(英文版)》1999,17(5):449-456
1.IntroductionTosolvelargesparsesystemsoflinearandnonlinearequationsonthemultiprocessorsystems,manyauthorspresentedandstudiedvariousparalleliterativemethodsinthesenseofmultisplittinginrecentyears.FOrdetailsonecanreferto[1]-[9]andreferencestherein.Amo... 相似文献
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Xi Yang 《计算数学(英文版)》2014,(6):696-720
This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations (DAEs). Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs. 相似文献
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本文介绍求解线性常系数微分代数方程组的波形松弛算法, 基于Laplace积分变换得到该算法新的收敛理论. 进一步将波形松弛算法应用于求解非定常Stokes方程, 介绍并讨论了连续时间波形松弛算法CABSOR算法和离散时间波形松弛算法DABSOR算法. 相似文献
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Murat CANDAN 《数学物理学报(B辑英文版)》2014,(2):354-366
The class f of almost convergent sequences was introduced by G.G. Lorentz,using the idea of the anach limits [A contribution to the theory of divergent sequences,Acta Math. 80(1948), 167–190]. Let f0( ) and f( ) be the domain of the double sequential band matrix ( r, s) in the sequence spaces f0 and f. In this article, the β-and γ-duals of the space f( ) are determined. Additionally, we give some inclusion theorems concerning with the spaces f0( ) and f( ). Moreover, the classes(f( ) : μ) and(μ : f( )) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space. 相似文献
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WAVEFORM RELAXATION METHODS AND ACCURACY INCREASEWAVEFORMRELAXATIONMETHODSANDACCURACYINCREASE¥SongYongzhong(NanjingNormalUniv... 相似文献
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Yao-linJiang 《计算数学(英文版)》2005,23(1):49-66
In this paper we consider continuous-time and discrete-time waveform relaxation meth-ods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the convergence condition of the iterative methods by invoking the spec-tral theory on the resulting iterative operators. By use of the implicit difference forms,namely the backward-differentiation formulae, we also yield the convergence condition of the discrete waveforms. Numerical experiments are provided to illustrate the theoretical work reported here. 相似文献
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BAIZHONGZHI 《高校应用数学学报(英文版)》1998,13(1):45-52
The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473-486) is further investigated.The investigations show that these relaxation methods really have considerably larger convergence domains. 相似文献
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We present componentwise condition numbers for the problems of Moore-Penrose generalized matrix inversion and linear least squares. Also, the condition numbers for these condition numbers are given. 相似文献
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王永俊 《高等学校计算数学学报(英文版)》2005,14(4):325-329
In this paper we prove that the asymptotic rate of convergence of the modified Gauss-Seidel method of a non-singular M-matrix is a monotonic function for 1 precondition parameters 0 ≤ αi≤1/2, (i = 1,2,... ,n - 1). 相似文献
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The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results confirm the theoretical prediction of the exponential rate of convergence. The result in this work seems to be the first successful spectral approach (with theoretical justification) for the Volterra type equations. 相似文献