摘要
对于线性代数方程组Ａｘ＝ｂ的求解，Ｇａｕｓｓ－Ｓｅｉｄｅｌ迭代算法并不能保证对所有的ｎ×ｎ矩阵Ａ都收敛．本文通过向Ｇａｕｓｓ－Ｓｅｉｄｅｌ算法中加入松驰因子而导出一种松驰迭代算法，并且给出了收敛性定理及其证明．该算法对所有的对称正定矩阵Ａ都具有收敛性，拓宽了Ｇａｕｓｓ－Ｓｅｉｄｅｌ方法的使用范围．
The Gauss-Seidel iterative method for solving a set of linear algebraic equation Ax = b does not ensure convergence for all n × n matrix A. In this paper, we present a relaxation iterative method by adding relaxation factor into Gauss-Seidel iterative method and give convergence theorem and its proof, so that it can converge for all symmetric positive-definite matrices A. Thus we expand the applicability of Gauss-Seidel iterative method.
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
1995年第2期159-162,共4页
Journal of Central China Normal University：Natural Sciences
关键词
线性代数方程组
收敛性
G-S法
linear algebraic equations
Gauss--Seidel method
relaxation iterative method
symmetric positive--definite matrices
convergence
