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October 2009 Numerical Verification Methods for Spherical $t$-Designs
Xiaojun Chen
Japan J. Indust. Appl. Math. 26(2-3): 317-325 (October 2009).


The construction of spherical $t$-designs with $(t+1)^2$ points on the unit sphere $S^2$ in $\mathbb{R}^3$ can be reformulated as an underdetermined system of nonlinear equations. This system is highly nonlinear and involves the evaluation of a degree $t$ polynomial in $(t+1)^4$ arguments. This paper reviews numerical verification methods using the Brouwer fixed point theorem and Krawczyk interval operator for solutions of the underdetermined system of nonlinear equations. Moreover, numerical verification methods for proving that a solution of the system is a spherical $t$-design are discussed.


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Xiaojun Chen. "Numerical Verification Methods for Spherical $t$-Designs." Japan J. Indust. Appl. Math. 26 (2-3) 317 - 325, October 2009.


Published: October 2009
First available in Project Euclid: 1 February 2010

zbMATH: 1184.65049
MathSciNet: MR2589478

Keywords: spherical designs , system of nonlinear equations , verification

Rights: Copyright © 2009 The Japan Society for Industrial and Applied Mathematics

Vol.26 • No. 2-3 • October 2009
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