Papers › Interpolation by integrals on balls
Interpolation by integrals on balls
Ludovico Bruni Bruno, Giacomo Elefante
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In this work we blend interpolation theory with numerical integration, constructing an interpolator based on integrals over n-dimensional balls. We show that, under hypotheses on the radius of the n-balls, the problem can be treated as an interpolation problem both on a collection of (n-1)-spheres Sⁿ⁻¹ and multivariate point sets, for which a wide literature is available. With the aim of exact quadrature and cubature formulae, we offer a neat strategy for the exact computation of the Vandermonde matrix of the problem and propose a meaningful Lebesgue constant. Problematic situations are evidenced and a charming aspect is enlightened: the majority of the theoretical results only deal with the centre of the domains of integration and are not really sensitive to their radius. We flank our theoretical results by a large amount of comprehensive numerical examples.
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