一类舒尔补矩阵的条件数分析  

ANALYSIS ABOUT CONDITION NUMBER OF A CLASS SCHUR COMPLEMENT MATRIX

作　　者：钟尔杰[1] 黄廷祝[1] 

机构地区：[1]电子科技大学应用数学学院,成都610054

出　　处：《数值计算与计算机应用》2008年第2期89-95,共7页Journal on Numerical Methods and Computer Applications

摘　　要：研究了一类线性方程组系数矩阵的红黑排序方法,以及由红黑排序矩阵导出的舒尔补矩阵的条件数.利用三对角矩阵的特征值分析方法推导了一类块三对角矩阵的特征值和条件数,构造了三对角矩阵和块三对角矩阵的红黑排序排列矩阵,利用矩阵相似变换推导出红黑排序矩阵中的舒尔补的特征值和条件数表达式.理论分析和数值试验结果均表明这类舒尔补矩阵具有更好的性质.The red and black ordering method about the coefficient matrix of a class of linear equations and the condition number of schur complement matrix deduced from red and black matrix are studied. By the eigenvalue analysis in tri-diagonal matrix, the eigenval ues and condition numbers of a class block tri-diagonal matrix have been gained. The ordering matrixes of the tri-diagonal matrix and block tri-diagonal matrix have been constructed. The application of matrix similarity transformation has deduced the eigen value and the expressions of condition number of schur matrix. The results of the analysis and the numerical experiment have showed that the schur complement matrix will have better property.

关 键 词：三对角矩阵 块三对角矩阵 红黑排序 舒尔补矩阵 条件数 

分 类 号：O151.21[理学—数学]