一类改进的鞍点矩阵最大特征值的区间估计  

An Improved Interval Estimate for the Maximum Eigenvalues of Saddle Point Matrices

作　　者：李铮[1] 张铁[1] 李长军[1] 

机构地区：[1]东北大学理学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2009年第9期1362-1364,1368,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(10771031)

摘　　要：对鞍点矩阵的特征值估计理论进行了研究.基于对鞍点矩阵的对称性以及鞍点矩阵的最大特征值与子矩阵特征值之间关系的分析,改进了关于鞍点矩阵最大特征值的下界估计,从而得到一类改进的关于鞍点矩阵最大特征值的区间估计.数值实验中考察了由P1-P0混合有限元方法离散化Stokes方程所导出鞍点矩阵的最大特征值.数值结果表明所给出的关于鞍点矩阵最大特征值的区间估计是有效的.The eigenvalue estimate theory of saddle point matrices is studied. Estimate for the lower bound of the maximum eigenvalues of saddle point matrices is improved, based on the analysis of the symmetry of saddle point matrices and the relation between maximum eigenvalues of saddle point matrices and the eigenvalues of their sub-matrices. Then, an improved interval estimate for the maximum eigenvalues of saddle point matrices is obtained. The maximum eigenvalues of saddle point matrices, which are derived from the stationary Stokes equation discretized by the P1 -P0 mixed finite element method, are observed in the numerical experiment. The numerical results demonstrate that the involved interval estimate for the maximum eigenvalues of saddle point matrices is valid.

关 键 词：鞍点矩阵 特征值 区间估计 混合有限元法 STOKES方程 

分 类 号：O241.6[理学—计算数学] O241.8[理学—数学]