Name
Abstract | ||
|---|---|---|
In the present paper, we consider the approximation of the solution of an ill-posed spherical pseudo-differential equation at a given point. While the methods for approximating the whole solution are well-studied in Hilbert spaces, such as the space of square-summable functions, the computation of values of the solution at given points is much less studied. This can be explained, in particular, by the fact that for square-summable functions the functional of pointwise evaluation is, in general, not well defined. To overcome this limitation we adjust the regularized least-squares method of An, Chen, Sloan and Womersley [1] by using a special a posteriori parameter choice rule. We also illustrate our theoretical findings by numerical results for the reconstruction of the solution at a given point. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1515/cmam-2015-0006 | COMPUTATIONAL METHODS IN APPLIED MATHEMATICS |
Keywords | DocType | Volume |
Spherical Pseudo-Differential Equations,Balancing Principle,Spherical Harmonics,Regularization | Journal | 15 |
Issue | ISSN | Citations |
2 | 1609-4840 | 1 |
PageRank | References | Authors |
0.38 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sergei V. Pereverzyev | 1 | 20 | 4.29 |
| Pavlo Tkachenko | 2 | 8 | 4.26 |