Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem
نویسندگان
چکیده
منابع مشابه
A Refined Second-order Arnoldi (RSOAR) Method for the Quadratic Eigenvalue Problem and Implicitly Restarted Algorithms
To implicitly restart the second-order Arnoldi (SOAR) method proposed by Bai and Su for the quadratic eigenvalue problem (QEP), it appears that the SOAR procedure must be replaced by a modified SOAR (MSOAR) one. However, implicit restarts fails to work provided that deflation takes place in the MSOAR procedure. In this paper, we first propose a Refined MSOAR (abbreviated as RSOAR) method that i...
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A deeation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses the Ritz value approximations of the eigenvalues of A converge at diierent rates. A numerically stable scheme is introduced that implicitly deeates the converged approximations from the iteratio...
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This report provides an introductory overview of the numerical solution of large scale algebraic eigenvalue problems. The main focus is on a class of methods called Krylov subspace projection methods. The Lanczos method is the premier member of this class and the Arnoldi method is a generalization to the nonsymmetric case. A recently developed and very promising variant of the Arnoldi/Lanczos s...
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متن کاملImplicitly Restarted Generalized Second-order Arnoldi Type Algorithms for the Quadratic Eigenvalue Problem
We investigate the generalized second-order Arnoldi (GSOAR) method, a generalization of the SOAR method proposed by Bai and Su [SIAM J. Matrix Anal. Appl., 26 (2005): 640–659.], and the Refined GSOAR (RGSOAR) method for the quadratic eigenvalue problem (QEP). The two methods use the GSOAR procedure to generate an orthonormal basis of a given generalized second-order Krylov subspace, and with su...
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ژورنال
عنوان ژورنال: East Asian Journal on Applied Mathematics
سال: 2018
ISSN: 2079-7362,2079-7370
DOI: 10.4208/eajam.070517.180917a