块对角占优矩阵Schur补的块对角占优度和特征值分布

Block Biagonally Dominant Degree and Eigenvalue Distribution for Schur Complements of Block Diagonally Dominant Matrices

给出了I(II)-型块对角占优矩阵Schur补的块对角占优度的新估计式,运用其得到了块对角占优矩阵Schur补的特征值的新分布区域,改进了近期文献中的相应结果.最后,用算例对所得理论结果进行了说明.

Some new estimations of block diagonally dominant degree for the schur complement of I（II）-block diagonally dominant ma- trices are given. By applying the estimations, we present new inclusion regions for eigenvalues of the Schur complement of block diago- nally dominant matrices. And it is proved that these results improve the corresponding those in [ Liu et al, Theorems on Schur comple- ment of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems [ J ]. Linear Algebra Appl,2011,435 ：3085 -3100. ]. Finally, a numerical example is given to illustrate the theory results.