Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems. Issue 3 (August 2014)

• Record Type: Journal Article
• Authors: Yin, Jun-Feng; Yin, Guo-Jian
• Is Part Of: Numerical mathematics. Volume 7:Issue 3(2014)
• Page Start: 399
• Page End: 412
• Publication Date: 2014-08
• Subjects: 65F10, -- 65F15, -- 15A06, -- 15A18; Shifted linear systems, -- full orthogonalization method, -- restarted Arnoldi process, -- deflation, -- collinear; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.1017/S1004897900000179
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: In this paper, we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations. Theoretical analysis shows that with the deflation technique, the new residual of shifted restarted FOM is still collinear with each other. Hence, the new approach can solve the shifted systems simultaneously based on the same Krylov subspace. Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.