Diagonal Matrix And Generalized Diagonally Dominant Matrix Numerical Analysis

This paper investigates Explicit inverse of a five-diagonal matrix by the elements of special twisted decompositions and generalized equidiagonal-dominant matrix and its applications. There are three chapters in this paper altogether.In chapter 1, knowledge of background and relative notations of the paper is introduced.In chapter 2, fast algorithm for the elements of the inverse of a five-diagonal matrix are presented. The results are obtained by relationships between the elements of the inverse and the elements of special twisted decompositions of it. and some results can also be extended to block five-diagonal matrices.In chapter 3, the concept of generalized equidiagonal-dominant matrix is introduced and a necessary and sufficient condition for a non-singular H matrix is obtained. Moreover we obtain an upper bound of || A^-1 ||_∞ for a triangular matrix.