Title: Asymptotic analysis of numerical steepest descent with path approximations
Authors: Asheim, Andreas
Huybrechs, Daan
Issue Date: Mar-2009
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW536
Abstract: We propose a variant of the numerical method of steepest descent for oscillatory integrals by using a low-cost explicit polynomial approximation of the paths of steepest descent. A loss of asymptotic order is observed, but in the most relevant cases the overall asymptotic order remains higher than a truncated asymptotic expansion at similar computational effort. Theoretical results based on number theory underpinning the mechanisms behind this effect are presented.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section

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