一类新的预条件USSOR迭代法的收敛性比较  

Convergence comparison of a new type of preconditioned USSOR iteration method

作　　者：李慧芳 畅大为[1] 吕玉芳 LI Huifang;CHANG Dawei;LV Yufang(School of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《纺织高校基础科学学报》2018年第4期497-502,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11226266;11401361)

摘　　要：为了提高线性方程组Ax=b迭代方法的收敛速度,提出一类新的预条件矩阵P1=I+S1,并在该预条件下提出新的USS OR迭代方法.当系数矩阵A是非奇异M-阵时,运用矩阵分裂理论得到新的预条件USSOR迭代法的谱半径不大于传统USSOR迭代法的谱半径,并得到新的预条件USSOR迭代法的收敛性.最后举例说明上述结论.In order to improve the convergence rate of the iterative method of linear equations Ax=b,a new preconditioned matrix P1=I+S1 is proposed,and a new USSOR iteration method is proposed under the precondition.When the coefficient matrix A is a nonsingular M matrix,the spectral radius of the new preconditioned USSOR iteration method is not larger than the spectral radius of the traditional USSOR iteration method by using the matrix splitting theory,and the convergence of the new preconditioned USSOR iteration method is obtained.Finally,an example is given to illustrate the above conclusions.

关 键 词：M-阵 预条件 USSOR迭代法 谱半径 矩阵分裂理论 

分 类 号：O241.6[理学—计算数学] TP301.1[理学—数学]