Accelerating the Induced Dimension Reduction method using spectral information

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:345

Article

Astudillo, R.¹  de Gier, J. M.²  van Gijzen, M. B.¹ 

[1] Delft Univ Technol, Delft Inst Appl Math, Van Mourik Broekmanweg 6, NL-2628 XE Delft, Netherlands

[2] TNO Tech Sci, Distributed Sensor Syst, Oude Waalsdorperweg 63, NL-2597 AK The Hague, Netherlands

关键词: Induced Dimension Reduction method;    System of linear equations;    Sequence of systems of linear equation;    Eigenvalues and eigenvectors;   

DOI  :  10.1016/j.cam.2018.06.014

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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