Solving shifted linear systems with restarted GMRES augmented with error approximations. (15th September 2019)

• Record Type: Journal Article
• Authors: Wang, Rui-Rui; Niu, Qiang; Tang, Xiao-Bin; Wang, Xiang
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 6(2019)
• Page Start: 1910
• Page End: 1918
• Publication Date: 2019-09-15
• Subjects: Added linear systems -- Restarted GMRES -- Krylov subspace methods; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.03.037
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we investigate a variant of the restarted GMRES method for solving a series of large sparse linear systems. Restarting is carried out by augmenting Krylov subspaces with some recently generated error approximations from the seed system. The method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix–vector multiplication per iteration. Compared with solving each added linear system separately, the advantage of the new scheme is to lower down the overall cost of solving all added linear systems. Numerical experiments illustrate the efficiency of the acceleration strategy.