A new shift strategy for the implicitly restarted generalized\\ second-order Arnoldi method
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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The need to determine a few eigenvalues of a large sparse generalised eigenvalue problem Ax = λBx with positive semidefinite B arises in many physical situations, for example, in a stability analysis of the discretised Navier-Stokes equation. A common technique is to apply Arnoldi’s method to the shift-invert transformation, but this can suffer from numerical instabilities as is illustrated by ...
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We study an inexact implicitly restarted Arnoldi (IRA) method for computing a few eigenpairs of generalized non-Hermitian eigenvalue problems with spectral transformation, where in each Arnoldi step (outer iteration) the matrix-vector product involving the transformed operator is performed by iterative solution (inner iteration) of the corresponding linear system of equations. We provide new pe...
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The explicitly restarted Arnoldi method (ERAM) can be used to find some eigenvalues of large and sparse matrices. However, it has been shown that even this method may fail to converge. In this paper, we present two new methods to accelerate the convergence of ERAM algorithm. In these methods, we apply two strategies for the updated initial vector in each restart cycles. The implementation of th...
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ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2016
ISSN: 1674-7216
DOI: 10.1360/012016-22