Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm
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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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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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1999
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10197-0