关键词: 迭代法, 广义G-函数, 谱半径

Abstract: For solving a system of linear equations with the form of Ax=b,it often splits A into A=M-N, Where M is nonsingular. It is known that x(k+1)=M-1Nx(k)+M-1b (k=0,1,2,…) converges to the solution x=A-1b for each x(0) if and only if spectral radius ρ(M-1N)＜1. The matrix M-1N　is called an iterative matrix.　It is easy to see the estimates for bounds of 　ρ(M-1N)　are interested.A concept of G-functions introduced by Hoffman and Nowosad was introduced to generalized G-functions,and the concept generalized Gfunctions were applied to obtain the bounds for moduli eigenvalues of the iterative matrices. The bounds for spectral radii of iterative matrices M-1N were obtained and applied for solving linear systems. The obtained results improve the known corresponding results.　Finally, a numerical example was given for illustrating the advantage of the results.

Key words: iteration, generalized G-function, eigenvalue, spectral radius