Volume 25, pp. 101-114, 2006.

Quadrature-free quasi-interpolation on the sphere

M. Ganesh and H. N. Mhaskar


We construct certain quasi-interpolatory operators for approximation of functions on the sphere, using tensor product scattered data satisfying certain symmetry conditions. Our operators are constructed without using any quadrature formulas. We use instead a special class of orthonormal bivariate trigonometric polynomials. These polynomials are functions on the sphere, and are constructed in a numerically stable way, based on the data locations. The quasi-interpolatory operators give near best approximation to every continuous function. We demonstrate our constructions numerically with several benchmark functions using randomly generated data locations.

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Key words

function approximation on the sphere, scattered data, quasi-interpolation, Jacobi matrices

AMS subject classifications

42A15, 65D32, 33C55

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