The construction of cubature formulae for a family of integrals: A bifurcation problem

DOI10.1007/BF02276917zbMath0668.65018OpenAlexW2521754183WikidataQ57779024 ScholiaQ57779024MaRDI QIDQ1118348

Ann Haegemans, Ronald Cools, Dirk Roose, Pierre Verlinden

Publication date: 1988

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02276917

zbMATH Keywords

symmetrybifurcationcontinuationcubature formula

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

The construction of cubature formulae by continuation, Chebyshev lattices, a unifying framework for cubature with Chebyshev weight function, Minimal cubature formulae of degree 2k-1 for two classical functionals

Uses Software

• AUTO
• AUTO-86

Cites Work

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• Another step forward in searching for cubature formulae with a minimal number of knots for the square
• Automatic computation of knots and weights of cubature formulae for circular symmetric planar regions
• On the numerical solution of non-linear equations characterizing minimal cubature formulae
• Kubaturformeln mit minimaler Knotenzahl
• A locally parameterized continuation process
• Economical symmetrical quadrature rules for complete polynomials over a square domain
• The Application of Integer Programming to the Computation of Fully Symmetric Integration Formulas in Two and Three Dimensions
• Construction of Algebraic Cubature Rules Using Polynomial Ideal Theory
• Perfectly Symmetric Two-Dimensional Integration Formulas with Minimal Numbers of Points