Numerical verification methods for spherical \(t\)-designs

DOI10.1007/BF03186537zbMath1184.65049OpenAlexW2007330164MaRDI QIDQ849181

Xiaojun Chen

Publication date: 25 February 2010

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

Full work available at URL: https://projecteuclid.org/euclid.jjiam/1265033784

zbMATH Keywords

verificationsystem of nonlinear equationsspherical designsBrouwer fixed point theoremunderdetermined systemKrawczyk interval operator

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Interval and finite arithmetic (65G30) Other designs, configurations (05B30) Applications of design theory to circuits and networks (94C30) Algorithms with automatic result verification (65G20)

Uses Software

• INTLAB
• INTOPT_90
• mctoolbox

Cites Work

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• A variational characterisation of spherical designs
• Averaging sets: A generalization of mean values and spherical designs
• Spherical codes and designs
• Fast verification of solutions of matrix equations
• Rigorous global search: continuous problems
• Extremal systems of points and numerical integration on the sphere
• Newton-like methods for solving underdetermined nonlinear equations with nondifferentiable terms
• McLaren's improved snub cube and other new spherical designs in three dimensions
• Equidistribution on the Sphere
• Spherical faraday cage for the case of equal point charges and chebyshev-type quadrature on the sphere
• Existence of Solutions to Systems of Underdetermined Equations and Spherical Designs
• Optimal Numerical Integration on a Sphere
• How good can polynomial interpolation on the sphere be?

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