Double Diagonally Dominant Degree of Schur Complement of the Strictly Double Diagonally Dominant Matrix and Its Application
Matrix Schur complement is an important part of matrix theory and its application,which has a wide application background.Strictly double diagonally dominant matrices are a very important class of special matrices,which are closely related to fluid mechanics calculation,material simulation and design,electromagnetic field calculation and so on.The study of strictly double diagonally dominant matrices mainly focuses on two aspects:eigenvalue localization of Schur complement of strictly double diagonally dominant matrices;Infinite norm estimation of inverse of Schur complement of strictly double diagonally dominant matrices.First,a new lower bound estimation of the double diagonally dominant degree of Schur complement of strictly double diagonally dominant matrices is given.Then,the new eigenvalue inclusion set of Schur complement of strictly double diagonally dominant matrices and the new upper bound of infinite norm for the inverse of Schur complement of strictly diagonally dominant matrices are obtained by using the obtained estimations.Numerical examples show that the results obtained in this paper improve some existing results.
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