The relaxed gradient based iterative algorithm for solving matrix equations AiXBi=Fi. (1st August 2017)

• Record Type: Journal Article
• Authors: Sheng, Xingping; Sun, Weiwei
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 3(2017)
• Page Start: 597
• Page End: 604
• Publication Date: 2017-08-01
• Subjects: Matrix equations -- Relaxed gradient based iterative algorithm -- Relaxation factor -- Numerical solution; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.05.008
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we first present a relaxed gradient based iterative (RGI) algorithm for solving matrix equations A 1 X B 1 = F 1 and A 2 X B 2 = F 2 . The idea is from (Niu et al., 2011; Xie and Ma, 2016) in which efficient algorithms were developed for solving the Sylvester matrix equations. Then the RGI algorithm is extended to solve the generalized linear matrix equations of the form A i X B i = F i, ( i = 1, 2, …, N ) . For any initial value, it is proved that the iterative solution converges to their true solution under some appropriate assumptions. Finally, a numerical example is given to illustrate that the introduced iterative algorithm is more efficient than gradient based maximal convergence rate iterative (GI) algorithm of Ding et al. (2010) in speed, elapsed time and iterative steps.