Computing almost minimal formulas on the square

DOI10.1016/j.cam.2012.05.021zbMath1247.65032OpenAlexW1991517889MaRDI QIDQ442711

Mattia Festa, Alvise Sommariva

Publication date: 3 August 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2012.05.021

zbMATH Keywords

cubaturesquaremultivariate integrationminimal rules

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (4)

Compression of Multivariate Discrete Measures and Applications ⋮ The infinite convergence order of near minimal cubature formulas on classes of periodic functions ⋮ Schemes for cubature over the unit disk found via numerical optimization ⋮ PI-type fully symmetric quadrature rules on the 3-, \dots, 6-simplexes

Uses Software

• Matlab
• Optimization Toolbox
• Polygint

Cites Work

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• Polynomial interpolation and cubature over polygons
• Computing Fekete and Lebesgue points: Simplex, square, disk
• Improved cubature formulae of high degrees of exactness for the square
• Asymmetric cubature formulas for polynomial integration in the triangle and square
• A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions
• Nontensorial Clenshaw-Curtis cubature
• Lagrange interpolation on Chebyshev points of two variables
• On the (non)-existence of some cubature formulas: Gaps between a theory and its applications
• An encyclopaedia of cubature formulas.
• Symmetric quadrature rules on a triangle
• Monomial cubature rules since ``Stroud: A compilation. II
• A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
• Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra
• Construction of Algebraic Cubature Rules Using Polynomial Ideal Theory
• Generalized Gaussian quadrature rules on arbitrary polygons
• A Cardinal Function Algorithm for Computing Multivariate Quadrature Points

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