一类新的预条件USSOR迭代法的比较定理  

Comparison theorem of a new preconditioned USSOR iterative method

作　　者：杨青青[1] 畅大为[1] 董瑾[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安陕西710062

出　　处：《纺织高校基础科学学报》2013年第4期507-510,共4页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(60671063)

摘　　要：提出一种新的预条件矩阵,并给出基于该预条件的USSOR迭代法.比较了系数矩阵为不可约L阵时,在新的预条件下USSOR迭代法和传统USSOR迭代法谱半径的大小.预条件加快了传统的USSOR迭代法的收敛速度,并得到新的比较定理.且新方法的谱半径严格小于传统方法的谱半径.最后通过数值例子验证了所得结论的正确性.A novel preconditioned matrix and a new Un-Symmetrical Successive Over Relaxation （USSOR） itera- rive method base on this preconditioned matrix are proposed in this paper. The spectral radius of the new and the traditional USSOR iterative method were compared when coefficient matrix was irreducible. The result demon- strates that the new method accelerates the speed of convergency. And a new comparison theorem is got, distin- guished with other methods, the comparison inequality of spectral radius is a strict inequality. Finally two nu- merical examples are given to demonstrate the correctness of the new method.

关 键 词：L矩阵 USSOR迭代方法 预条件 谱半径 

分 类 号：O241.6[理学—计算数学]