APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS  

作　　者：邵新慧 沈海龙 李长军 

机构地区：[1]Department of Mathematics,Northeastern University,Shenyang 110004,P.R.China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2006年第8期1115-1121,共7页应用数学和力学（英文版）

基　　金：Project supported by the Natural Science Foundation of Liaoning Province of China (No.20022021)

摘　　要：Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method （GAOR） is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method （GAOR） is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.

关 键 词：stair matrices iterative method parallel computation generalization of the AOR method 

分 类 号：O241[理学—计算数学]