A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems. Issue 1 (31st January 2017)

• Record Type: Journal Article
• Authors: Miao, Cun-Qiang
• Is Part Of: East Asian journal on applied mathematics. Volume 7:Issue 1(2017)
• Page Start: 21
• Page End: 37
• Publication Date: 2017-01-31
• Subjects: 15A18, -- 65F15, -- 65F50, -- 34L15, -- 65N25; Symmetric eigenproblem, -- filtering technique, -- Chebyshev polynomials, -- Krylov subspace, -- Davidson-type method; Applied mathematics -- Periodicals; 519.05
• DOI: 10.4208/eajam.160816.131016a
• Languages: English
• ISSNs: 2079-7362

Abstract

Abstract: For symmetric eigenvalue problems, we constructed a three-term recurrence polynomial filter by means of Chebyshev polynomials. The new filtering technique does not need to solve linear systems and only needs matrix-vector products. It is a memory conserving filtering technique for its three-term recurrence relation. As an application, we use this filtering strategy to the Davidson method and propose the filtered-Davidson method. Through choosing suitable shifts, this method can gain cubic convergence rate locally. Theory and numerical experiments show the efficiency of the new filtering technique.