Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
نویسندگان
چکیده
منابع مشابه
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
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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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 propose an accelerating method for the restarted Arnoldi iteration to compute a number of eigenvalues of the standard eigenproblem Ax = x and discuss the dependence of the convergence rate of the accelerated iteration on the distribution of spectrum. The e ectiveness of the approach is proved by numerical results. We also propose a new parallelization technique for the nonsymmetric double sh...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 1996
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s0895479895281484