期刊
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
卷 10, 期 6, 页码 647-671出版社
SPRINGER
DOI: 10.1007/s10208-010-9068-y
关键词
Oscillatory quadrature; Steepest descent; Numerical integration
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.
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