van der Vorst, Henk A.; Ye, Qiang Residual replacement strategies for Krylov subspace iterative methods for the convergence of true residuals. (English) Zbl 0983.65039 SIAM J. Sci. Comput. 22, No. 3, 835-852 (2000). This paper presents a residual replacement scheme for improving the convergence in finite-precision Krylov subspace methods to solve linear systems. The new scheme replaces the approximate residual with the true residual intermittently. It is simple and can be added to existing Krylov subspace iterative solvers to improve convergence. An error analysis and numerical tests are included. Reviewer: F.Uhlig (Auburn) Cited in 1 ReviewCited in 15 Documents MSC: 65F10 Iterative numerical methods for linear systems 65G50 Roundoff error Keywords:Krylov subspace method; residual vector; finite precision; residual replacement; convergence; error analysis; numerical tests Software:Harwell-Boeing sparse matrix collection; BiCGstab PDFBibTeX XMLCite \textit{H. A. van der Vorst} and \textit{Q. Ye}, SIAM J. Sci. Comput. 22, No. 3, 835--852 (2000; Zbl 0983.65039) Full Text: DOI