Moment-free numerical integration of highly oscillatory functions

By Sheehan Olver. 2006

203 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2ca8da6a2226f12fac6c23d2b1a75578eb9a7818

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Numerical approximation of vector-valued highly oscillatory integrals (2007, methodology): “In [7], it was noted that choosing a certain basis causes the asymptotic order to increase without the need for nontrivial multiplicities.”
Moment-free numerical approximation of highly oscillatory integrals with stationary points (2007, methodology): “In Levin’s collocation method [6] and Levin-type methods [8], a solution to an equation of this form was numerically approximated using collocation, but neither of these methods are accurate when stationary points are present.”
Fast, numerically stable computation of oscillatory integrals with stationary points (2010, methodology): “1 in [24] states that if pω, p ′ ω = O ( ω−α ) and 0 = pω(±1) = · · · = p ω (±1), then Iω[pω] = O ( ω−s−α−1 ) .”
An improved Levin quadrature method for highly oscillatory integrals (2010, methodology): “Olver [17] believes that the system of linear equations in the Levin-type method will be well-conditioned if the frequency ω is large enough.”
Highly Oscillatory Quadrature: The Story soFar (2006, methodology): “We dwell no further on this issue, referring the reader to ( Olver 2005a ).”
From high oscillation to rapid approximation I: Modified Fourier expansions (2008, methodology): “25 Following the discussion in (Iserles & Nørsett 2004), we need to chooseδ small enough so thatmδ 1 for the firstm modified Fourier coefficients.”
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation (2006, methodology): “Methods have been devised that compute an accurate approximation to the value of the integral with low computational complexity and with a number of operations that actually decreases as ω increases to infinity [12, 13, 14, 15, 16, 17, 18].”