H-矩阵及其比较矩阵的预条件Gauss-Seidel法的收敛性  

Convergence of Preconditioned Gauss-Seidel Method for H-matrix and Its Comparison Matrix

作　　者：周婷[1] 郭文彬[1] 

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《烟台大学学报（自然科学与工程版）》2011年第4期260-263,共4页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(10771073)

摘　　要：讨论了新的预条件矩阵下的预条件Gauss-Seidel法.在更广义的分裂条件下,将此法应用于H-矩阵及其比较矩阵上,并得到了相应的收敛结果和谱半径的比较结果,从而说明应用于H-矩阵的预条件Gauss-Seidel法的收敛速度要比应用于它的比较矩阵的预条件Gauss-Seidel法的收敛速度快.最后,给出一个数值例子验证得到的结果.Under a new preconditioned matrix,the preconditioned Gauss-Seidel method is discussed.In a more general split conditions,this method is applied to H-matrix and its comparison matrix,the corresponding convergence results and the comparison results of the spectral radius are obtained.This shows that the convergence rate of the preconditioned Gauss-Seidel method corresponding to H-matrix is faster than that of the preconditioned Gauss-Seidel method corresponding to its comparison matrix.Finally,a numerical example is also given to illustrate the results.

关 键 词：预条件Gauss-Seidel法 H-矩阵 比较矩阵 

分 类 号：O241.6[理学—计算数学]