Asymptotic Analysis of Numerical Steepest Descent with Path Approximations

作者：Asheim Andreas^*; Huybrechs Daan

来源：Foundations of Computational Mathematics, 2010, 10(6): 647-671.

DOI：10.1007/s10208-010-9068-y

• 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.

• 出版日期2010-12