Matrix Multisplitting Methods with Applications to Linear Complementarity Problems∶ Parallel Asynchronous Methods
Matrix Multisplitting Methods with Applications to Linear Complementarity Problems∶ Parallel Asynchronous Methods
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DOI：
10.1080/00207160211927
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发表时间：
2002-01
影响因子：
1.8
通讯作者：
Z. Bai;D. J. Evans
中科院分区：
文献类型：
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作者：
Z. Bai;D. J. Evans
我们考虑使用并行矩阵多重分裂方法来解决线性互补问题，该方法找到实数向量 z ] R n ，使得 Mz + q S 0、z S 0 和 z T ( Mz + q )=0，其中 M ] R n 2 n 是给定的实数矩阵，q ] R n 是给定的实数向量。综述了最近发展的基于问题定点变换、系统显式投影和矩阵隐式分裂的并行异步多重分裂迭代方法；讨论了它们对于某些典型矩阵类的渐近收敛性质；并对其内部关系进行了研究。因此，为解决现代高速多处理器系统上的大稀疏线性互补问题，提出了多分裂意义上的系统算法模型和渐进收敛意义上的可靠理论保证。本文是 Bai 和 Evans [18] 最近工作的延续，其中包括并行同步和混沌矩阵多重分裂迭代方法及其收敛理论。
We consider parallel matrix multisplitting methods for solving linear complementarity problem that finds a real vector z ] R n such that Mz + q S 0, z S 0 and z T ( Mz + q )=0, where M ] R n 2 n is a given real matrix and q ] R n a given real vector. The recently developed parallel asynchronous multisplitting iterative methods based on fixed-point transformation of the problem, explicit projection of the system and implicit splittings of the matrix are reviewed; their asymptotic convergence properties for some typical matrix class are discussed; and their internal relationships are studied. Therefore, systematic algorithmic models in the sense of multisplitting and reliable theoretical guarantees in the sense of asymptotic convergence are presented for solving the large sparse linear complementarity problems on modern high-speed multiprocessor systems. This paper is a continuity of the recent work of Bai and Evans [18] , which includes the parallel synchronous and chaotic matrix multisplitting iterative methods and their convergence theories.