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      Nested Krylov methods for shifted linear systems

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      time-harmonic wave equation, inner-outer Krylov methods, flexible preconditioning, Shifted linear systems

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          Abstract

          Most algorithms for the simultaneous solution of shifted linear systems make use of the shift-invariance property of the underlying Krylov spaces. This particular comes into play when preconditioning is taken into account. We propose a new iterative framework for the solution of shifted systems that uses an inner multi-shift Krylov method as a preconditioner within a flexible outer Krylov method. Shift-invariance is preserved if the inner method yields collinear residuals.

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          Journal
          10.14293/P2199-8442.1.SOP-MATH.PGMQPO.v1

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