A unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations
From the authors' abstract and introduction: We set up a unified framework for the construction of various asynchronous parallel matrix multisplitting iterative methods for solving the large sparse system of linear equations, suitable to the SIMD and MIMD multiprocessor systems, respectively. Following suitable constructions of the linear operators, proper choices of the weighting matrices and reasonable constraints of the delayed information involved in this framework, not only all the known synchronous parallel matrix multisplitting iterative methods, can be recovered, and also a series of efficient new ones can be yielded. Hence, this framework has great generality and summarization. On the other hand, this framework itself is also an improved and generalized asynchronous parallel matrix multisplitting iterative method for the system of linear equations. Since the mutual wait, as well as the frequent communication among the processors of the MIMD multiprocessor system, are avoided in the implementation of this method, it can do useful numerical computations. This hence, makes this new method able to attain considerably high parallel computational efficiency in practical applications. Under rather weak conditions, we establish general criteria for determining the convergence, as well as the divergence, of this new framework. At last, we show how the known matrix multisplitting methods can be classified in this new framework, and what novel ones can be yielded by it, too.
parallel matrix multisplitting iterative methods
scientific article; zbMATH DE number 1002358