Volume 25, pp. 1-16, 2006.
Bivariate interpolation at Xu points: results, extensions and applications
Len Bos, Marco Caliari, Stefano De Marchi, and Marco Vianello
Abstract
In a recent paper, Y. Xu proposed a set of Chebyshev-like
points for polynomial interpolation on the square . We
have recently proved that the Lebesgue constant of these points
grows like of the degree (as with the best known
points for the square), and we have implemented an accurate
version of their Lagrange interpolation formula at
linear cost. Here we construct non-polynomial Xu-like interpolation
formulas on bivariate compact domains with various geometries,
by means of composition with suitable smooth transformations.
Moreover, we show applications of Xu-like interpolation to the
compression of surfaces given as large scattered data sets.
Full Text (PDF) [2 MB],
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Key words
bivariate polynomial interpolation, Xu points, Lebesgue constant, domains transformations, generalized rectangles, generalized sectors, large scattered data sets, surface compression
AMS subject classifications
65D05
