PARALLEL QUASI-CHEBYSHEV ACCELERATION TO NONOVERLAPPING MULTISPLITTING ITERATIVE METHODS BASED ON OPTIMIZATION  

作　　者：Ruiping Wen GuoyanMeng Chuanlong Wang 

机构地区：[1]Higher Education Key Laboratory of Engineering Science Computing in Shanxi Province, Taiyuan NormaZ University, Taiyuan 030012, China [2]Department of Computer Science, Xinzhou Normal University, Xinzhou 034000, China [3]Higher Education Key Laboratory of Engineering Science Computing in Shanxi Province, Taiyuan Normal University, Taiyuan 030012, China

出　　处：《Journal of Computational Mathematics》2014年第3期284-296,共13页计算数学（英文）

摘　　要：In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonover- lapping multisplitting iterative method for the linear systems when the coefficient matrix is either an H-matrix or a symmetric positive definite matrix. First, m parallel iterations are implemented in m different processors. Second, based on l1-norm or l2-norm, the m opti- mization models are parallelly treated in m different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numeri- cal examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonover- lapping multisplitting iterative method for the linear systems when the coefficient matrix is either an H-matrix or a symmetric positive definite matrix. First, m parallel iterations are implemented in m different processors. Second, based on l1-norm or l2-norm, the m opti- mization models are parallelly treated in m different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numeri- cal examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.

关 键 词：Parallel quasi-Chebyshev acceleration Nonoverlapping multisplitting iterative method Convergence optimization. 

分 类 号：O241.6[理学—计算数学] TP18[理学—数学]