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arXiv · 1501.02090

Parameter choice strategies for least-squares approximation of noisy smooth functions on the sphere

Sergei. V. Pereverzyev·Ian. H. Sloan·Pavlo Tkachenko
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Abstract

We consider a polynomial reconstruction of smooth functions from their noisy values at discrete nodes on the unit sphere by a variant of the regularized least-squares method of An et al., SIAM J. Numer. Anal. 50 (2012), 1513--1534. As nodes we use the points of a positive-weight cubature formula that is exact for all spherical polynomials of degree up to $2M$, where $M$ is the degree of the reconstructing polynomial. We first obtain a reconstruction error bound in terms of the regularization parameter and the penalization parameters in the regularization operator. Then we discuss a priori and a posteriori strategies for choosing these parameters. Finally, we give numerical examples illustrating the theoretical results.

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Sergei. V. Pereverzyev, Ian. H. Sloan, Pavlo Tkachenko. 2015-01-09. Parameter choice strategies for least-squares approximation of noisy smooth functions on the sphere. https://arxiv.org/abs/1501.02090

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