Approximation of eigenfunctions in kernel-based spaces. (English) Zbl 1353.65139
The authors study the approximation of eigenfunctions in kernel-based spaces. They use the approximation error that is bounded in terms of generalized power functions and use determination of error-optimal \(n\)-dimensional subspaces. The authors prove that eigenspaces minimize the \(L_{2}(\Omega)\) norm of the power function. Several examples are given to illustrate the numerical technique via a greedy point selection strategy. In addition they show that the algorithm provided allows to approximate the eigenvalues for Sobelev spaces in a way that recovers the true decay rates.
Reviewer: Seenith Sivasundaram (Daytona Beach)
MSC:
| 65R20 | Numerical methods for integral equations |
| 45C05 | Eigenvalue problems for integral equations |
Keywords:
Mercer kernels; radial basis functions; eigenfunctions; eigenvalues; \(n\)-widths; optimal subspaces; greedy methods; kernel-based spaces; generalized power functions; algorithmReferences:
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