迭代法迭代阵谱半径新上界

A New Upper Bound for the Spectral Radius of Iterative Matrices

引用双严格对角占优的概念,针对线性方程组bAx=在求数值解时常用的迭代方法,给出了Jacobi和Gauss-Seidel迭代法迭代阵谱半径的新上界,该新上界优于严格对角占优矩阵条件下得到的已有的结果,是已有结果在更广泛矩阵类条件下的推广,对相应迭代法迭代阵谱半径的估计更加精确。最后给出了数值例子说明所给结果的优越性。

Jacobi and Gauss-Seidel iterations for solving large linear system bAx= are studied. Based on the concept of the doubly diagonal dominance, new upper bound for the spectral radius of Jacobi and Gauss-Seidel iterations are presented. Results obtained improve the known corresponding results and are suited to extended matrices. Finally, two numerical examples are given for illustrating advantage results in this paper.