Orthogonal polynomials and Gaussian quadrature for refinable weight functions

DOI10.1016/j.acha.2004.06.002zbMath1064.42023OpenAlexW1994680478MaRDI QIDQ704214

Dirk P. Laurie, Johan M. de Villiers

Publication date: 13 January 2005

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

Full work available at URL: https://doi.org/10.1016/j.acha.2004.06.002

zbMATH Keywords

orthogonal polynomialsrefinable functionGaussian quadratureLegendre seriesmodified moments

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) General harmonic expansions, frames (42C15) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)

Related Items

Triangular Bernstein moment-based identification of algebraic curves ⋮ Direct and inverse computation of Jacobi matrices of infinite iterated function systems ⋮ Refinable functions, functionals, and iterated function systems ⋮ Gauss-type quadrature rule with complex nodes and weights for integrals involving Daubechies scale functions and wavelets ⋮ Computation of quadrature rules for integration with respect to refinable functions on assigned nodes ⋮ An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures ⋮ Orthogonal polynomials for refinable linear functionals

Uses Software

• CLN

Cites Work

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• Gauss quadrature for refineable weight functions
• On refinable functions and subdivision with positive masks
• An algorithm for Gaussian quadrature given modified moments
• On Refinement Equations Determined by Pólya Frequency Sequences
• Quadrature Formulae and Asymptotic Error Expansions for Wavelet Approximations of Smooth Functions
• Calculation of Gauss Quadrature Rules
• Construction of Gauss-Christoffel Quadrature Formulas
• A recurrence scheme for converting from one orthogonal expansion into another

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