文献类型：期刊文献

英文题名：Convergence Results on Iteration Algorithms to Linear Systems

作者：Wang, Zhuande[1];Yang, Chuansheng[2];Yuan, Yubo[3]

机构：[1]Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China;[2]Zhejiang Ocean Univ, Dept Math, Zhoushan 316000, Zhejiang, Peoples R China;[3]E China Univ Sci & Technol, Sch Informat Sci & Engn, Shanghai 200237, Peoples R China

年份：2014

外文期刊名：SCIENTIFIC WORLD JOURNAL

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000336308400001)】；

基金：The work is partially supported by National Nature Science Foundation of China (1117105, 11101071, and 61001200) and the Fundamental Research Funds for the centeral Universities (ZYGX2009J103).

语种：英文

摘要：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.