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Sommariva, A.; Vianello, M.

Near-optimal polynomial interpolation on spherical triangles. (English) Zbl 1504.65025

Mediterr. J. Math. 19, No. 2, Paper No. 68, 17 p. (2022).
Summary: We compute Chebyshev-like norming grids for polynomials on spherical triangles. The construction is based on a conjecture about norming grids for univariate trigonometric polynomials (supported by wide numerical testing), together with the fundamental notion of Dubiner distance for multivariate compact sets. Such grids can be used to extract Fekete-like interpolation points with slowly increasing Lebesgue constant, by basic numerical linear algebra.

MSC:

65D05 Numerical interpolation
41A10 Approximation by polynomials

Keywords:

spherical triangles; trigonometric polynomials; spherical polynomials; Dubiner distance; Chebyshev norming grids; Fekete-like points; polynomial interpolation

Software:

dCATCH; Algorithm 623
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\textit{A. Sommariva} and \textit{M. Vianello}, Mediterr. J. Math. 19, No. 2, Paper No. 68, 17 p. (2022; Zbl 1504.65025)
Full Text: DOI

References:

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