Title: Complex Gaussian quadrature of oscillatory integrals
Authors: DeaƱo Cabrera, Alfredo *
Huybrechs, Daan * # ×
Issue Date: Apr-2009
Publisher: Springer
Series Title: Numerische Mathematik vol:112 issue:2 pages:197-219
Abstract: We construct and analyze Gauss-type quadrature rules with complex- valued nodes and weights to approximate oscillatory integrals with stationary points of high order. The method is based on substituting the original interval of integration by a set of contours in the complex plane, corresponding to the paths of steepest descent. Each of these line integrals shows an exponentially decaying behaviour, suitable for the application of Gaussian rules with non-standard weight functions. The results differ from those in previous research in the sense that the constructed rules are asymptotically optimal, i.e., among all known methods for oscillatory integrals they deliver the highest possible asymptotic order of convergence, relative to the required number of evaluations of the integrand.
ISSN: 0029-599X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
* (joint) first author
× corresponding author
# (joint) last author

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