Alternating stationary iterative methods based on double splittings. (1st May 2021)

• Record Type: Journal Article
• Authors: Nandi, Ashish Kumar; Shekhar, Vaibhav; Mishra, Nachiketa; Mishra, Debasisha
• Is Part Of: Computers & mathematics with applications. Volume 89(2021)
• Page Start: 87
• Page End: 98
• Publication Date: 2021-05-01
• Subjects: Iterative methods -- Alternating scheme -- Proper splitting -- Moore–Penrose inverse -- Non-negativity -- Convergence theorem; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.02.015
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Matrix double splitting iterations are simple in implementation while solving real non-singular (rectangular) linear systems. In this paper, we present two Alternating Double Splitting (ADS) schemes formulated by two double splittings and then alternating the respective iterations. The convergence conditions are then discussed along with comparative analysis. The set of double splittings used in each ADS scheme induces a preconditioned system which helps in showing the convergence of the ADS schemes. We also show that the classes of matrices for which one ADS scheme is better than the other, are mutually exclusive. Numerical experiments confirm that the proposed ADS schemes have several computational advantages over the existing methods. Though the problems are considered in the rectangular matrix settings, the same problems are even new in non-singular matrix settings.