The Sdd ~ + Matrix And The H-matrix Algorithm

This paper is concerned with two classes of important matrices: symmetric diagonally dominant matrix ( SDD+ matrix) and generalized diagonally dominant matrix( H - matrix). Because of the characters of itself, such as sparsity, the matrix will be stored and computed in different ways. So algorithms designed should be different. This paper is devoted to improve the algorithms of finding the nearest symmetric diagonally dominant matrix for a given matrix and judging wheather a given matirix is an H - matrix or not.This paper mainly includes two parts:1. Minimizing the distance from a given matrix to the set of symmetric and diagonally domiant matrices is valueful in computer graphics. To solve this problem, recently proposed Primal algorithm, Polar algorithm and selective alternating projections. Compared with Primal algorithm, selective alternating projections produces a siginificant reduction in CPU time, however, the precision is reduced, too. In this paper, we refurbish the set of index to improve the algorithm, the advantages and disadvantages of those algorithms are compared through Matlab programs, the result indicates that the improved algorithm advanced the precision.2. We extend and improve one algorithm to solve the problem of determining whether a matrix is generalized diagonally dominant or not. A new algorithm is proposed which is suited for reducible matrices, numerical evidence for the effectiveness of the proposed algorithm is presented, while the matrix is spare, the improved algrithm advanced computational time.