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Shifted GMRES for oscillatory integrals

Numerische Mathematik volume 114, pages 607–628 (2010)Cite this article

Abstract

None of the existing methods for computing the oscillatory integral \({\int_a^b f(x){\rm e}^{{\rm i}\omega g(x)}{\rm d}x}\) achieve all of the following properties: high asymptotic order, stability, avoiding deformation into the complex plane and insensitivity to oscillations in f. We present a new method that satisfies these properties, based on applying the gmres algorithm to a shifted linear differential operator.

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  1. Oxford University Computing Laboratory, Numerical Analysis Group, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK

    Sheehan Olver

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  1. Sheehan Olver
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Olver, S. Shifted GMRES for oscillatory integrals. Numer. Math. 114, 607–628 (2010). https://doi.org/10.1007/s00211-009-0264-0

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  • DOI: https://doi.org/10.1007/s00211-009-0264-0

Mathematics Subject Classification (2000)

  • 65D32