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.
Near-Optimal Polynomial Interpolation on Spherical Triangles
Sommariva A.;Vianello M.
2022
Abstract
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.File in questo prodotto:
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