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TW 536
Andreas Asheim and Daan Huybrechs
Asymptotic analysis of numerical steepest descent with path approximations
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.
report.pdf (277K) / mailto: D. Huybrechs