1. Accelerating the Induced Dimension Reduction method using spectral information.
- Author
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Astudillo, R., De Gier, J.M., and Van Gijzen, M.B.
- Subjects
- *
REDUCTION potential , *LINEAR equations , *EIGENVALUE equations , *RITZ method , *APPLIED mathematics - Abstract
Abstract The Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, 2008) is a short-recurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using spectral information. We construct a Hessenberg relation from the IDR(s) residual recurrences formulas, from which we approximate the eigenvalues and eigenvectors. Using the Ritz values, we propose a self-contained variant of the Ritz-IDR(s) method (Simoncini and Szyld, 2010) for solving a system of linear equations. In addition, the Ritz vectors are used to speed-up IDR(s) for the solution of sequence of systems of linear equations. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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