title: Convergence results on iteration algorithms to linear systems.
abstract: In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.
authors.affiliation: School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.
authors.forename: Zhuande
authors.initials: Z
authors.lastname: Wang
authors.affiliation: Department of Mathematics, Zhejiang Ocean University, Zhoushan, Zhejiang 316000, China.
authors.forename: Chuansheng
authors.initials: C
authors.lastname: Yang
authors.affiliation: School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China.
authors.forename: Yubo
authors.initials: Y
authors.lastname: Yuan
mesh_terms: D000465:Algorithms; D016014:Linear Models