Name
Title | ||
|---|---|---|
Parameter Choice Strategies for Least-squares Approximation of Noisy Smooth Functions on the Sphere |
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), pp. 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. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140964990 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
spherical polynomial,parameter choice strategy,regularization,penalization,continuous function on the sphere,a posteriori rules | Least squares,Mathematical optimization,Polynomial,Mathematical analysis,A priori and a posteriori,Reconstruction error,Regularization (mathematics),Operator (computer programming),Mathematics,Unit sphere | Journal |
Volume | Issue | ISSN |
53 | 2 | 0036-1429 |
Citations | PageRank | References |
2 | 0.41 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sergei V. Pereverzyev | 1 | 20 | 4.29 |
| Ian H. Sloan | 2 | 1180 | 183.02 |
| Pavlo Tkachenko | 3 | 8 | 4.26 |