Least-squares polynomial approximation on weakly admissible meshes: Disk and triangle

Authors:
Len Bos;Alvise Sommariva;Marco Vianello
Affiliations:
Department of Computer Science, University of Verona, Italy;Department of Pure and Applied Mathematics, University of Padova, Italy;Department of Pure and Applied Mathematics, University of Padova, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 6
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Abstract

We construct symmetric polar WAMs (weakly admissible meshes) with low cardinality for least-squares polynomial approximation on the disk. These are then mapped to an arbitrary triangle. Numerical tests show that the growth of the least-squares projection uniform norm is much slower than the theoretical bound, and even slower than that of the Lebesgue constant of the best known interpolation points for the triangle. As opposed to good interpolation points, such meshes are straightforward to compute for any degree. The construction can be extended to polygons by triangulation.