Efficient computation of oscillatory integrals via adaptive multiscale local Fourier bases

DOI10.1006/acha.2000.0305zbMath0958.65148OpenAlexW1969569206MaRDI QIDQ1577560

Elena Braverman, Moshe Israeli, Ronald R. Coifman, Avram Sidi, Amir Z. Averbuch

Publication date: 30 March 2001

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/3164b81e0a3be453ff09df31c8f81b76b483e049

zbMATH Keywords

Fourier transformquadrature formulasoscillatory kerneltrapezoidal rulemultiscale adaptive local cosine transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items

Fast Algorithms for High Frequency Wave Propagation ⋮ Asymptotic Fourier coefficients for a \(C^\infty\) bell (smoothed-``top-hat) \& the Fourier extension problem ⋮ Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles ⋮ A hierarchical butterfly LU preconditioner for two-dimensional electromagnetic scattering problems involving open surfaces ⋮ Scattering in flatland: Efficient representations via wave atoms ⋮ A characterization of \(L^p(\mathbb R )\) by local trigonometric bases with \(1<p<\infty\) ⋮ Optimized local trigonometric bases with nonuniform partitions ⋮ Fast Algorithms for Boundary Integral Equations ⋮ LCT-WAVELET BASED ALGORITHMS FOR DATA COMPRESSION ⋮ A Multiscale Butterfly Algorithm for Multidimensional Fourier Integral Operators ⋮ Directional Preconditioner for 2D High Frequency Obstacle Scattering

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Modulated Malvar-Wilson bases
• Quadrature methods for periodic singular and weakly singular Fredholm integral equations
• Diagonal forms of translation operators for the Helmholtz equation in three dimensions
• Fast numerical computations of oscillatory integrals related to acoustic scattering. I
• Local cosine transform -- A method for the reduction of the blocking effect in JPEG
• Brushlets: A tool for directional image analysis and image compression
• Gaussian bases
• Optimized local trigonometric bases
• Fast wavelet transforms and numerical algorithms I
• Orthonormal bases of compactly supported wavelets
• Biorthogonal bases of compactly supported wavelets
• Entropy-based algorithms for best basis selection
• Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations
• Improving the accuracy of quadrature method solutions of Fredholm integral equations that arise from nonlinear two-point boundary value problems