Tuned preconditioners for inexact two‐sided inverse and Rayleigh quotient iteration |
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Authors: | Melina A Freitag Patrick Kürschner |
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Institution: | 1. Department of Mathematical Sciences, University of Bath, Claverton Down, BA2 7AY, UK;2. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstra?e 1, Magdeburg, Germany |
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Abstract: | Convergence results are provided for inexact two‐sided inverse and Rayleigh quotient iteration, which extend the previously established results to the generalized non‐Hermitian eigenproblem and inexact solves with a decreasing solve tolerance. Moreover, the simultaneous solution of the forward and adjoint problem arising in two‐sided methods is considered, and the successful tuning strategy for preconditioners is extended to two‐sided methods, creating a novel way of preconditioning two‐sided algorithms. Furthermore, it is shown that inexact two‐sided Rayleigh quotient iteration and the inexact two‐sided Jacobi‐Davidson method (without subspace expansion) applied to the generalized preconditioned eigenvalue problem are equivalent when a certain number of steps of a Petrov–Galerkin–Krylov method is used and when this specific tuning strategy is applied. Copyright © 2014 John Wiley & Sons, Ltd. |
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Keywords: | two‐sided (in)exact Rayleigh quotient iteration inexact inverse iteration convergence rate preconditioning Krylov subspace methods Bi‐conjugated gradients two‐sided Jacobi– Davidson method |
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