IMPLICITLY RESTARTED GENERALIZED SECOND-ORDER ARNOLDI TYPE ALGORITHMS FOR THE QUADRATIC EIGENVALUE PROBLEM
نویسندگان
چکیده
منابع مشابه
Implicitly 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...
متن کاملA 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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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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We first introduce a second-order Krylov subspace Gn(A,B;u) based on a pair of square matrices A and B and a vector u. The subspace is spanned by a sequence of vectors defined via a second-order linear homogeneous recurrence relation with coefficient matrices A and B and an initial vector u. It generalizes the well-known Krylov subspace Kn(A;v), which is spanned by a sequence of vectors defined...
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2015
ISSN: 2224-6851,1027-5487
DOI: 10.11650/tjm.1.2015.4577