Two Problems, The Matrix Calculation

In this paper, we discuss two problems for the matrix computation. The first is matrix perturbation analysis, and the second is matrix iterative analysis. In the first chapter, we study the perturbation for the matrix generalized Cholesky factorization, and present the bounds of additive and multiplicative perturbations, which improve and extend the results of paper[3]. In the second chapter, we study the modified Gauss-Seidel method, and present some sufficient conditions so that the MGS method converges, which improve and extend the results of paper[8].