Lower Bound Estimation Of Generalized Strictly Bidiagonally Dominant Matrix ?(A^-1) And Its Triangular-Schur Complement

Diagonally dominant matrices are of great value in numerical computation,linear control theory and matrix theory.In addition,when solving the linear equations Ax=b,it is often necessary to estimate the infinite norm or spectral radius of the coefficient matrix A.In recent years,many mathematicians have studied some special diagonally dominant matrices and obtained many important conclusions.Based on these conclusions,the lower bounds of the spectral radii of the inverse matrices of generalized strictly doubly diagonally dominant matrices are estimated,and the triangle Schur complement of generalized strictly doubly diagonally dominant matrices is proved to be strictly diagonally dominant matrices(When the order is greater than 2,it is a generalized strictly doubly diagonally dominant matrix).The specific contents are as follows:In the first chapter,the existing research on diagonally dominant matrices and strictly diagonally dominant matrices is briefly described.Secondly,make a rough introduction to the content of this paper.In the second chapter,firstly,the infinite norm and spectral radius of inverse matrices of different diagonally dominant matrices are introduced.Secondly,a new definition of generalized strictly doubly diagonally dominant matrix is given.By using the properties of some strictly diagonally dominant matrices and the relation between infinite norm and spectral radius,the lower bound of spectral radius of the inverse matrix of generalized strictly diagonally dominant matrices is estimated and verified by numerical examples.In the third chapter,the research status of Schur supplement was introduced.The definition of the triangular Schur complement(diagonal-Schur complement is its special case)is also derived.Using the properties of strictly doubly diagonally dominant matrices,and the proof method of Schur complement of generalized doubly diagonally dominant matrices,proves that trigonometric Schur complement of generalized strictly doubly diagonally dominant matrices is strictly diagonally dominant matrices.