Contributions To Transmissibility Of Diagonally Dominant Matrices And Estimates For Bounds For Spectral Radius Of Block Iterative Matrices Of Iterative Method

This paper mainly includes two parts:1. Contributions to Transmissibility of Diagonally Dominant Matrices: Wepresent some interesting sufficient conditions and sufficient necessary conditions,which generalize and improve the previous results. For example:In 2.1, we give some simple criteria for diagonally dominant matrices to benonsingular H-matrices:If diagonally dominant matrix A is a nonsingular H-matrix, then if and onlyif A[α] is also a nonsingular H-matrix, where A[α] is a principal submatrix of A thatlies in the rows and columns indexed by α(?){1,2,L n} , which is an interestingimprovement of the paper [9].In 2.2, we present another transmissibility of diagonally dominant matrices—property of positive definite. Some similar sufficient and necessary conditions areobtained. For example,If diagonally dominant matrix A is a positive definite matrix, then if and onlyif A[α] is also a positive definite matrix, where A[α] is the same as section 2.1.2. Estimates for bounds for spectral radius of block iterative matrices of blockiterative method: we give some new upper and lower bounds for the spectral radius ofblock iterative matrix ρ(M(-1)N), where M is respectively a block strictly diagonaldominant matrix and block double strictly diagonal dominant matrix. For example:In 3.1, For a block strictly diagonal dominant matrix M , we obtain...