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1.
Lili Zhang 《计算数学(英文版)》2015,33(1):100-112
To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based synchronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an $H_+$-matrix, which improve the existing convergence theory. Numerical results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation. 相似文献
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《应用数学与计算数学学报》2021,(1):107-122
In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as... 相似文献
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Min-Li Zeng & Guo-Feng Zhang 《数学研究》2015,48(1):1-17
In this paper, a modulus-based generalized skew-Hermitian triangular splitting
(MGSTS) iteration method is present for solving a class of linear complementarity
problems with the system matrix either being an $H_+$-matrix with non-positive
off-diagonal entries or a symmetric positive definite matrix. The convergence of the
MGSTS iteration method is studied in detail. By choosing different parameters, a series
of existing and new iterative methods are derived, including the modulus-based Jacobi
(MJ) and the modulus-based Gauss-Seidel (MGS) iteration methods and so on. Experimental
results are given to show the effectiveness and feasibility of the new method
when it is employed for solving this class of linear complementarity problems. 相似文献
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首先证明了M-矩阵的H-相容分裂都是正则分裂,反之不成立.这表明对于M-矩阵而言,其正则分裂包含H-相容分裂.然后针对系数矩阵为M-矩阵的线性互补问题,建立了两个收敛定理:一是模系多分裂迭代方法关于正则分裂的收敛定理;二是模系二级多分裂迭代方法关于外迭代为正则分裂和内迭代为弱正则分裂的收敛定理. 相似文献
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Chenliang Li Jinping Zeng 《高等学校计算数学学报(英文版)》2006,15(4):289-298
In this paper we consider some synchronous and asynchronous multisplitting and Schwarz methods for solving the linear complementarity problems. We establish some convergence theorems of the methods by using the concept of M-splitting. 相似文献
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Mezzadri Francesco Galligani Emanuele 《Journal of Optimization Theory and Applications》2022,193(1):598-620
Journal of Optimization Theory and Applications - In this paper, we generalize the projected Jacobi and the projected Gauss–Seidel methods to vertical linear complementarity problems (VLCPs)... 相似文献
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Chen-liang Li Jin-ping Zeng 《应用数学学报(英文版)》2007,23(1):79-90
We consider several synchronous and asynchronous multisplitting iteration schemes for solving aclass of nonlinear complementarity problems with the system matrix being an H-matrix.We establish theconvergence theorems for the schemes.The numerical experiments show that the schemes are efficient forsolving the class of nonlinear complementarity problems. 相似文献
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为了改进求解大型稀疏线性互补问题模系多重网格方法的收敛速度和计算时间,本文采用加速模系超松弛(AMSOR)迭代方法作为光滑算子.局部傅里叶分析和数值结果表明此光滑算子能有效地改进模系多重网格方法的收敛因子、迭代次数和计算时间. 相似文献
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Parallel Newton two-stage iterative methods to solve nonlinear systems are studied. These algorithms are based on both the multisplitting technique and the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms studied, computational results about these methods on a distributed memory multiprocessor are discussed.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
14.
Josef Stoer 《Annals of Operations Research》2001,103(1-4):149-159
The paper is concerned with methods for solving linear complementarity problems (LCP) that are monotone or at least sufficient in the sense of Cottle, Pang and Venkateswaran (1989). A basic concept of interior-point-methods is the concept of (perhaps weighted) feasible or infeasible interior-point paths. They converge to a solution of the LCP if a natural path parameter, usually the current duality gap, tends to 0.After reviewing some basic analyticity properties of these paths it is shown how these properties can be used to devise also long-step path-following methods (and not only predictor–corrector type methods) for which the duality gap converges Q-superlinearly to 0 with an arbitrarily high order. 相似文献
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为了在并行和向量机上求解对称正定性方程且Ax=b,两组多分裂方法被考虑,中,把Galligain和Ruggiero的两级算术平均方法推广到两级多分裂方法并给出了一些合适的内分裂例子,同时讨论了所引起的两级多分裂方法的收敛性。 相似文献
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改进了奇异M-矩阵的线性方程组的并行多分裂法的一些最近结果,给出了并行多分裂迭代方法的一些收敛性的理论结果。 相似文献
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We present an interior-point method for monotone linear complementarity problems over symmetric cones (SCLCP) that is based
on barrier functions which are defined by a large class of univariate functions, called eligible kernel functions. This class
is fairly general and includes the classical logarithmic function, the self-regular functions, as well as many non-self-regular
functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the
iteration bounds for the entire class. We also calculate the iteration bounds of both large-step and short-step versions of
the method for ten frequently used eligible kernel functions. For some of them we match the best known iteration bound for
large-step methods, while for short-step methods the best iteration bound is matched for all cases. The paper generalizes
results of Lesaja and Roos (SIAM J. Optim. 20(6):3014–3039, 2010) from P
∗(κ)-LCP over the non-negative orthant to monotone LCPs over symmetric cones. 相似文献
19.
By further generalizing the skew-symmetric triangular splitting iteration method studied by Krukier, Chikina and Belokon (Applied Numerical Mathematics, 41 (2002), pp. 89–105), in this paper, we present a new iteration scheme, called the modified skew-Hermitian triangular splitting iteration method, for solving the strongly non-Hermitian systems of linear equations with positive definite coefficient matrices. We discuss the convergence property and the optimal parameters of this new method in depth. Moreover, when it is applied to precondition the Krylov subspace methods like GMRES, the preconditioning property of the modified skew-Hermitian triangular splitting iteration is analyzed in detail. Numerical results show that, as both solver and preconditioner, the modified skew-Hermitian triangular splitting iteration method is very effective for solving large sparse positive definite systems of linear equations of strong skew-Hermitian parts. 相似文献