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Title: Numerical verification methods for sphericalt -designs
Authors: Chen, X 
Keywords: Verification
Spherical designs
System of nonlinear equations
Issue Date: 2009
Publisher: Springer
Source: Japan journal of industrial and applied mathematics, 2009, v. 26, no. 2-3, p. 317-325 How to cite?
Journal: Japan journal of industrial and applied mathematics
Abstract: The construction of sphericalt-designs with (t+1)2 points on the unit sphereS 2 in ℝ3 can be reformulated as an underdetermined system of nonlinear equations. This system is highly nonlinear and involves the evaluation of a degreet 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 sphericalt-design are discussed.
ISSN: 0916-7005 (print)
1868-937X (online)
DOI: 10.1007/BF03186537
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