Numerical Integration of Highly Oscillating Functions
From MaRDI portal
Publication:3193162
DOI10.1007/978-1-4939-0258-3_23zbMath1325.65040OpenAlexW1853237464WikidataQ115058692 ScholiaQ115058692MaRDI QIDQ3193162
Gradimir V. Milovanović, Marija P. Stanić
Publication date: 15 October 2015
Published in: Analytic Number Theory, Approximation Theory, and Special Functions (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-1-4939-0258-3_23
numerical examplenumerical integrationGaussian quadraturescontour integration methodexponential-fitting quadrature rulesFilon-type quadratureshighly oscillating functionsweighted Fourier integrals
Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)
Related Items
Оптимальные квадратурные формулы в пространстве W2(m,m−1) периодических функций, Complexity of oscillatory integrals on the real line, OPTIMAL QUADRATURE FORMULAS FOR FOURIER COEFFICIENTS IN <i>W</i><sub>2</sub><sup>(<i>m</i>,<i>m</i>-1)</sup> 2 SPACE, Application of optimal quadrature formulas for reconstruction of CT images, Construction of optimal quadrature formulas for Fourier coefficients in Sobolev space \(L_{2}^{(m)}(0,1)\), On an optimal quadrature formula for approximation of Fourier integrals in the space \(L_2^{( 1 )}\)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Numerical approximations to integrals with a highly oscillatory Bessel kernel
- Analysis of a collocation method for integrating rapidly oscillatory functions
- A high order, progressive method for the evaluation of irregular oscillatory integrals
- Moebius inversion of Fourier transforms
- Numerical quadrature for Bessel transformations
- Suitable Gauss and Filon-type methods for oscillatory integrals with an algebraic singularity
- An improved Levin quadrature method for highly oscillatory integrals
- Numerical analysis of a fast integration method for highly oscillatory functions
- Orthogonal polynomials for modified Gegenbauer weight and corresponding quadratures
- Modified Clenshaw-Curtis method for the computation of Bessel function integrals
- On the error term of the Filon quadrature formulae
- A method for computing Bessel function integrals
- Numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures
- Operations on oscillatory functions
- Two robust methods for irregular oscillatory integrals over a finite range
- Extended quadrature rules for oscillatory integrands
- A method to generate generalized quadrature rules for oscillatory integrals
- Computation of irregularly oscillating integrals
- Quadrature rules using first derivatives for oscillatory integrands
- Exponentially fitted quadrature rules of Gauss type for oscillatory integrands
- Orthogonal polynomials and Gaussian quadrature rules related to oscillatory weight functions
- Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight
- Fast integration of rapidly oscillatory functions
- Interpolatory quadrature rules for oscillatory integrals
- Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday
- Integrating oscillatory functions in \texttt{Matlab}. II.
- Gaussian quadratures for oscillatory integrands
- On generalized quadrature rules for fast oscillatory integrals
- Numerical approximation of Fourier-transforms
- On quadrature methods for highly oscillatory integrals and their implementation
- Orthogonal Polynomials with Respect to Modified Jacobi Weight and Corresponding Quadrature Rules of Gaussian Type
- Integrating oscillatory functions in M<scp>atlab</scp>
- Orthogonal polynomials related to the oscillatory: Chebyshev weight function
- An expansion method for irregular oscillatory integrals
- On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
- Interpolation Processes
- Orthogonal polynomials for the oscillatory-Gegenbauer weight
- Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
- On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators
- On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
- Iterative Solution of Nonlinear Equations in Several Variables
- Remarks on an expansion for integrals of rapidly oscillating functions
- Efficient quadrature of highly oscillatory integrals using derivatives
- Moment-free numerical integration of highly oscillatory functions
- Numerical Calculation of Integrals with Strongly Oscillating Integrand
- The calculation of Fourier Coefficients
- Numerical integration with weight functions $\cos kx$, $\sin kx$ on $[0, 2\pi/t$, $t=1,2,\dots$]
- A Simple "Filon-Trapezoidal" Rule
- Numerical calculation of fourier integrals with cubic splines
- Construction of Gauss-Christoffel Quadrature Formulas
- The Calculation of Fourier Coefficients by the Mobius Inversion of the Poisson Summation Formula. Part I: Functions whose Early Derivatives are Continuous
- Gaussian Quadrature Formulas for the Integration of Oscillating Functions
- Gaussian Quadrature Formulas for the Evaluation of Fourier‐Cosine Coefficients
- A Modification of Filon's Method of Numerical Integration
- A Gauss quadrature rule for oscillatory integrands
