# American Institute of Mathematical Sciences

2012, 2(4): 863-873. doi: 10.3934/naco.2012.2.863

## On the convergence of generalized parallel multisplitting iterative methods for semidefinite linear systems

 1 Department of Mathematics, Changzhi University, Changzhi 046011, Shanxi Province, China 2 Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, Shanxi Province, China, China

Received  January 2012 Revised  October 2012 Published  November 2012

In this paper, we present the generalized stationary and nonstationary multisplitting iterative methods for positive semidefinite linear systems. We study the convergence theories of new methods and show that the quotient convergence and convergence of stationary parallel multisplitting method are equivalent under a concise condition. Finally, we prove that the generalized nonstationary parallel multisplitting method is quotient convergence with general weighting matrices.
Citation: Yanxing Cui, Chuanlong Wang, Ruiping Wen. On the convergence of generalized parallel multisplitting iterative methods for semidefinite linear systems. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 863-873. doi: 10.3934/naco.2012.2.863
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