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1.
一般二阶段多分裂迭代法的权矩阵都是预先给出的,在迭代过程中并不知道它的优劣.提出了广义的二阶段多分裂迭代法,它的加权矩阵不必预先给出,而是在迭代过程中通过求超平面上的最优解而得出的随迭代步数变化的动态的权矩阵.这样,动态的权矩阵能使得第k步的近似解更加逼近问题的真解.文中建立了新方法的收敛性理论,并以数值实验验证新方法的有效性. 相似文献
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本文结合具有共轭性的一种特殊多分裂与系数矩阵的稀疏性,提出求解系数矩阵为正定矩阵的线性方程组的并行多分裂迭代法.我们的新迭代法与标准迭代法不同点有两个方面:一是在我们的多分裂方法中只要求其中之一是收敛的分裂;二是权矩阵不必预先给出.这在并行计算中是很有效的算法.最后以数值实验验证新方法的有效性和可行性. 相似文献
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本文构造了求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法. 理论分析建立了新方法在系数矩阵为正定矩阵或H+矩阵时的收敛性质.数值实验结果表明新方法是行之有效的, 并且在最优参数下松弛two-sweep模系矩阵分裂迭代法在迭代步数和时间上均优于传统的模系矩阵分裂迭代法和two-sweep模系矩阵分裂迭代法. 相似文献
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本文针对广义绝对值方程,提出了基于牛顿法的矩阵多分裂方法.并在该方法的基础上进一步改进,得到了基于牛顿法的交替矩阵多分裂方法.给出两种算法在一定条件下的全局收敛性,并分析当分裂为H分裂时,基于牛顿法的矩阵多分裂方法的收敛条件.通过数值实验验证了所提出的算法的可行性和有效性. 相似文献
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奇异H-矩阵并行算法 总被引:2,自引:0,他引:2
1 引 言对于H矩阵类,到目前为止,人们关注的是非奇异H矩阵,对于奇异H矩阵研究结果很少,不象奇异M-矩阵研究的丰富[1-4]及获得了半收敛的一些结论,王川龙和游兆永将并行算法用于奇异M矩阵[5].本文的目的就是将并行算法用于奇异H矩阵.为此,首先讨论了奇异H矩阵与奇异M矩阵的关系.2 符号特征设Mn(R)代表实方阵的全体,A∈Mn(R),不特殊说明,A=D-B表示Jacobi分裂,〈A〉是A的比较矩阵,detA表示A的行列式,ρ(A)表示A的谱半径,μ(A)表示A的谱〈n〉={1,2,…,n},A[α|α]表示由α所决定的主子矩阵,α∈〈n〉.定理2.1[8] 设A是实H矩阵… 相似文献
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本文研究迭代求解非Hermitian正定线性方程组的问题.在系数矩阵HS分裂的基础上,提出了一种新的衍生并行多分裂迭代方法.通过参数调节分配反Hermitian部分给Hermitian部分的多分裂来衍生出非Hermitian正定系数矩阵的并行多分裂迭代格式,并利用优化技巧来获得权矩阵.同时,建立算法的收敛理论.最后用数值实验表明了新方法的有效性和可行性. 相似文献
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Chuan-Long Wang Guo-Yan Meng Xue-Rong Yong 《Advances in Computational Mathematics》2013,38(4):859-872
In this paper we present three modified parallel multisplitting iterative methods for solving non-Hermitian positive definite systems Ax?=?b. The first is a direct generalization of the standard parallel multisplitting iterative method for solving this class of systems. The other two are the iterative methods obtained by optimizing the weighting matrices based on the sparsity of the coefficient matrix A. In our multisplitting there is only one that is required to be convergent (in a standard method all the splittings must be convergent), which not only decreases the difficulty of constructing the multisplitting of the coefficient matrix A, but also releases the constraints to the weighting matrices (unlike the standard methods, they are not necessarily be known or given in advance). We then prove the convergence and derive the convergent rates of the algorithms by making use of the standard quadratic optimization technique. Finally, our numerical computations indicate that the methods derived are feasible and efficient. 相似文献
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In this work, we propose a new parallel multisplitting iterative method for non-symmetric positive definite linear systems. Based on optimization theory, the new method has two great improvements; one is that only one splitting needs to be convergent, and the other is that the weighting matrices are not scalar and nonnegative matrices. The convergence of the new parallel multisplitting iterative method is discussed. Finally, the numerical results show that the new method is effective. 相似文献
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In this paper, we generalize the nonstationary parallel multisplitting iterative method for solving the symmetric positive definite linear systems. With several choices of variable weighting matrices, the convergence properties of these generalized methods can be improved. Finally, the numerical comparison of several nonstationary parallel multisplitting methods are shown. 相似文献
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Summary. We present new theoretical results on two classes of multisplitting methods for solving linear systems iteratively. These
classes are based on overlapping blocks of the underlying coefficient matrix which is assumed to be a band matrix. We show that under suitable conditions the spectral radius of the iteration matrix does not depend on the weights of the method even if these weights are allowed to be negative. For a certain class of splittings
we prove an optimality result for with respect to the weights provided that is an M–matrix. This result is based on the fact that the multisplitting method can be represented by a single splitting
which in our situation surprisingly turns out to be a regular splitting. Furthermore we show by numerical examples that weighting
factors may considerably improve the convergence.
Received July 18, 1994 / Revised version received November 20, 1995 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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Fang Chen 《Applied mathematics and computation》2010,216(6):1771-1776
The multisplitting iteration method was presented by O’Leary and White [5] for solving large sparse linear systems on parallel multiprocessor system. In this paper, we further set up an asynchronous variant for the multisplitting iteration method with different weighting schemes studied by White [8]. Moreover, we establish a general convergence criterion for asynchronous iteration framework, and then prove the convergence of the new asynchronous multisplitting iteration method with different weighting schemes by making use of this general criterion. 相似文献
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In order to solve large sparse linear complementarity problems on parallel multiprocessor systems, we construct modulus-based synchronous two-stage multisplitting iteration methods based on two-stage multisplittings of the system matrices. These iteration methods include the multisplitting relaxation methods such as Jacobi, Gauss–Seidel, SOR and AOR of the modulus type as special cases. We establish the convergence theory of these modulus-based synchronous two-stage multisplitting iteration methods and their relaxed variants when the system matrix is an H ?+?-matrix. Numerical results show that in terms of computing time the modulus-based synchronous two-stage multisplitting relaxation methods are more efficient than the modulus-based synchronous multisplitting relaxation methods in actual implementations. 相似文献
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PARALLELNONLINEARMULTISPLITTINGRELAXATIONMETHODSWANGDERENANDBAIZHONGZHI(DepartmentofMathematics,ShanghaiUniversityofSciencean... 相似文献
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《Journal of Computational and Applied Mathematics》2002,138(2):287-296
Convergence properties of the nonstationary multisplitting two-stage iteration methods for solving large sparse system of linear equations are further studied when the coefficient matrices are hermitian positive definite matrices. 相似文献
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A CLASS OF GENERALIZED MULTISPLITTING RELAXATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS 总被引:1,自引:0,他引:1
BAIZHONGZHI 《高校应用数学学报(英文版)》1998,13(2):188-198
In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high-speed multiprocessor systems is set up. This class of methods not only includes all the existing relaxation methods for the linear complementarity problems ,but also yields a lot of novel ones in the sense of multisplittlng. We establish the convergence theories of this class of generalized parallel multisplitting relaxation methods under the condition that the system matrix is an H-metrix with positive diagonal elements. 相似文献