Efficient Computation of Oscillatory Integrals via Adaptive Multiscale Local Fourier Bases

A. Averbuch; E. Braverman; R. Coifman; M. Israeli; A. Sidi

doi:10.1006/acha.2000.0305

Efficient Computation of Oscillatory Integrals via Adaptive Multiscale Local Fourier Bases

A. Averbuch
, E. Braverman
, R. Coifman
, M. Israeli
, A. Sidi

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

The integral ∫₀^Le^iνφ(s,t)f(s)dswith a highly oscillatory kernel (large ν, ν is up to 2000) is considered. This integral is accurately evaluated with an improved trapezoidal rule and effectively transcribed using local Fourier basis and adaptive multiscale local Fourier basis. The representation of the oscillatory kernel in these bases is sparse. The coefficients after the application of local Fourier transform are smoothed. Sometimes this enables us to obtain further compression with wavelets.

Original language	English
Pages (from-to)	19-53
Number of pages	35
Journal	Applied and Computational Harmonic Analysis
Volume	9
Issue number	1
DOIs	https://doi.org/10.1006/acha.2000.0305
State	Published - Jul 2000
Externally published	Yes

Bibliographical note

Funding Information:
1This research is supported by a U.S.–Israel Binational Science Foundation grant for 1996–1999.

Funding

1This research is supported by a U.S.–Israel Binational Science Foundation grant for 1996–1999.

Funders
U.S.-Israel Binational Science Foundation

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10.1006/acha.2000.0305

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AU - Israeli, M.

AU - Sidi, A.

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Efficient Computation of Oscillatory Integrals via Adaptive Multiscale Local Fourier Bases

Abstract

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