標題: On the convergence of Ritz pairs and refined Ritz vectors for quadratic eigenvalue problems
作者: Huang, Tsung-Ming
Jia, Zhongxiao
Lin, Wen-Wei
應用數學系
Department of Applied Mathematics
關鍵字: Rayleigh-Ritz method;Ritz value;Ritz vector;Refined Ritz vector;Convergence
公開日期: 1-Dec-2013
摘要: For a given subspace, the Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the angle between the subspace and the desired eigenvector converges to zero. We prove that there is a Ritz value that converges to the desired eigenvalue unconditionally but the Ritz vector converges conditionally and may fail to converge. To remedy the drawback of possible non-convergence of the Ritz vector, we propose a refined Ritz vector that is mathematically different from the Ritz vector and is proved to converge unconditionally. We construct examples to illustrate our theory.
URI: http://dx.doi.org/10.1007/s10543-013-0438-0
http://hdl.handle.net/11536/23239
ISSN: 0006-3835
DOI: 10.1007/s10543-013-0438-0
期刊: BIT NUMERICAL MATHEMATICS
Volume: 53
Issue: 4
起始頁: 941
結束頁: 958
Appears in Collections:Articles


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