Numerical verification methods for spherical t-designs

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Abstract

The construction of spherical t-designs with (t + 1)2points on the unit sphere S2in ℝ3can 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)4arguments. 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.
Original languageEnglish
Pages (from-to)317-325
Number of pages9
JournalJapan Journal of Industrial and Applied Mathematics
Volume26
Issue number2-3
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Spherical designs
  • System of nonlinear equations
  • Verification

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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