柯西矩阵的三角分解及应用  

TRIANGULAR FACTORIZATION OF CAUCHY MATRIX AND ITS APPLICATION

作　　者：李琳[1] 袁修久[1] 赵学军[1] 

机构地区：[1]空军工程大学应用数学物理系,西安710051

出　　处：《高等学校计算数学学报》2011年第1期90-96,共7页Numerical Mathematics A Journal of Chinese Universities

基　　金：陕西省自然科学基金(2006A05)资助;陕西省电子信息系统综合集成重点实验基金资助

摘　　要：1引言矩阵分解具有非常重要的应用.例如,可以利用矩阵的LU分解回代求解线性方程组Ax=b.对于在有理函数的计算中经常遇到的以柯西矩阵为系数的线性方程组的求解问题,需要做柯西矩阵的三角分解.在[1]中给出了求柯西矩阵逆矩阵的算法,[2]是在[1]的基础上对求逆方程进一步修正,得到一种精度更高的方法.In this paper, a new method for triangular factorization of Cauchy matrix is proposed by decompositing the Cauchy matrix and its inverse into the product of some sparse lower and upper triangular matrices. This provides a theoretic foundation for further studying the fast algorithm of the numerical solutions of linear equations with the Cauchy matrix as its coefficient matrix. The method does not depend on the selection of the pivot and its arithematic operations is O（n2） which is fewer than the existing algorithms.

关 键 词：柯西矩阵 三角分解 应用 数值分析 

分 类 号：O241.6[理学—计算数学]