Moment-free numerical integration of highly oscillatory functions

Keywords

Mathematics, Numerical integration, Computation, Moment (physics), Applied mathematics

References

• Analysis of a collocation method for integrating rapidly oscillatory functionsDavid Levin — 1997
• Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)Milton Abramowitz, Irene A. Stegun, David S. Miller — 1965
• Errata: Handbook of mathematical functions with formulas, graphs, and mathematical tables (Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1964) by Milton Abramowitz and Irene A. StegunJackson B. Lackey, Henry C. Thatcher — 1977
• Approximation theory and methodsA.J. Davies — 1984
• Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.Chi C H, Milton Abramowitz, Irene A. Stegun — 1964
• Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables.D. E. Barton, Moses Abramovitz, I. A. Stegun — 1965
• Approximation Theory and Methods.Lars B. Wahlbin, M. J. D. Powell — 1982
• Efficient quadrature of highly oscillatory integrals using derivativesArieh Iserles, Syvert P. Nørsett — 2005
• Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical TablesD. B. Owen, Milton Abramowitz, Irene A. Stegun — 1965
• Norges Teknisk-naturvitenskapelige Universitet Efficient Quadrature of Highly Oscillatory Integrals Using Derivatives Efficient Quadrature of Highly Oscillatory Integrals Using DerivativesA. Iserles, S. P. Nørsett

Cited by

• From high oscillation to rapid approximation II: Expansions in polyharmonic eigenfunctionsArieh Iserles, Syvert P. Nørsett — 2006
• Efficient Computation of Highly Oscillatory Integrals by Using QTT Tensor ApproximationBoris N. Khoromskij, Alexander Veit — 2014
• Numerical Methods for Highly Oscillatory ProblemsAndreas Asheim — 2010
• Modified Fourier expansions: theory, construction and applicationsBen Adcock — 2010
• On the evaluation of highly oscillatory finite Hankel transform using special functionsZhenhua Xu, Shuhuang Xiang — 2016
• A Simpler GMRES Method for Oscillatory Integrals with IrregularOscillationsQinghua Wu, Meiying Xiang — 2015
• Numerical methods for systems of highly oscillatory ordinary differential equationsMarianna Khanamiryan — 2010
• Fluctuationless Univariate Integration Through Taylor Expansion with Remainder by Using Oscillatory Function Basis SetsN. A. Baykara, Ercan Gürvіt, Metin Demi̇ralp — 2009
• Numerical integration of bivariate functions using fluctuationlessness theorem with a trigonometric basis function to deal with highly oscillatory functionsErcan Gürvіt, N. A. Baykara, Metin Demi̇ralp — 2009
• Preconditioned GMRES for oscillatory integralsSheehan Olver — 2008
• From high oscillation to rapid approximation V: the equilateral triangleDaan Huybrechs, A. Iserles, Syvert P. Nørsett — 2011
• A comparative study of meshless complex quadrature rules for highly oscillatory integralsSirajul Islam, Uzma Nasib — 2015
• Numerical integration of multi-dimensional highly oscillatory integrals, based on eRPIMShahram Hosseini, Samira Smaeili — 2015
• A Sparse Discretization for Integral Equation Formulations of High Frequency Scattering ProblemsDaan Huybrechs, Stefan Vandewalle — 2007
• Anisotropic dynamics of optical vortex-beam propagating in biaxial crystals: a numerical method based on asymptotic expansion.Xiancong Lu, Lixiang Chen — 2013
• GMRES for the Differentiation OperatorSheehan Olver — 2009
• Asymptotic expansions and fast computation of oscillatory Hilbert transformsHaiyong Wang, Lun Zhang, Daan Huybrechs — 2011
• From high oscillation to rapid approximation III: multivariate expansionsA. Iserles, Syvert P. Nørsett — 2009
• On numerical computation of integrals with integrands of the form f(x)sin(w/xr) on [0, 1]A. Ihsan Hasçelik — 2009
• On the convergence rate of a modified Fourier seriesSheehan Olver — 2009

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