Numerical Quadrature and Nonlinear Sequence Transformations; Unified Rules for Efficient Computation of Integrals with Algebraic and Logarithmic Endpoint Singularities

DOI10.2307/2006199zbMath0441.41021OpenAlexW4249703828MaRDI QIDQ3882906

Publication date: 1980

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2006199

zbMATH Keywords

nonlinear sequence transformations Gaussian formulas numerical integration formulas for weight functions transformations of Levin

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximation by rational functions (41A20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Approximation to limiting values (summation of series, etc.) (40A25) Software, source code, etc. for problems pertaining to approximations and expansions (41-04)

Related Items (11)

Bi-orthogonality in rational approximation ⋮ Weights whose biorthogonal polynomials admit a Rodrigues formula ⋮ Some biorthogonal polynomials arising in numerical analysis and approximation theory ⋮ A comparative study of numerical steepest descent, extrapolation, and sequence transformation methods in computing semi-infinite integrals ⋮ Gaussian integration formulas for logarithmic weights and application to 2-dimensional solid-state lattices ⋮ Biorthogonal polynomials and numerical quadrature formulas for some finite-range integrals with symmetric weight functions ⋮ Positive interpolatory quadrature rules generated by some biorthogonal polynomials ⋮ Polynomials biorthogonal to dilations of measures, and their asymptotics ⋮ Asymptotic zero distribution of biorthogonal polynomials ⋮ On rates of acceleration of extrapolation methods for oscillatory infinite integrals ⋮ Zero distribution of composite polynomials and polynomials biorthogonal to exponentials

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