On spectral distribution of kernel matrices related to radial basis functions
This paper focuses on spectral distribution of kernel matrices related to radial basis functions. By relating a contemporary finite-dimensional linear algebra problem to a classical problem on infinite-dimensional linear integral operator, the paper shows how the spectral distribution of a kernel ma...
| Main Authors: | , |
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| Format: | Journal article |
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Springer Verlag
2015
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| _version_ | 1797095912857665536 |
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| author | Wathen, A Zhu, S |
| author_facet | Wathen, A Zhu, S |
| author_sort | Wathen, A |
| collection | OXFORD |
| description | This paper focuses on spectral distribution of kernel matrices related to radial basis functions. By relating a contemporary finite-dimensional linear algebra problem to a classical problem on infinite-dimensional linear integral operator, the paper shows how the spectral distribution of a kernel matrix relates to the smoothness of the underlying kernel function. The asymptotic behaviour of the eigenvalues of a infinite-dimensional kernel operator are studied from a perspective of low rank approximation—approximating an integral operator in terms of Fourier series or Chebyshev series truncations. Further, we study how the spectral distribution of interpolation matrices of an infinite smooth kernel with flat limit depends on the geometric property of the underlying interpolation points. In particularly, the paper discusses the analytic eigenvalue distribution of Gaussian kernels, which has important application on stably computing of Gaussian radial basis functions. |
| first_indexed | 2024-03-07T04:34:44Z |
| format | Journal article |
| id | oxford-uuid:cf8b4e82-e281-4c03-b6f3-7ff75f73c19b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:34:44Z |
| publishDate | 2015 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:cf8b4e82-e281-4c03-b6f3-7ff75f73c19b2022-03-27T07:43:17ZOn spectral distribution of kernel matrices related to radial basis functionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cf8b4e82-e281-4c03-b6f3-7ff75f73c19bSymplectic Elements at OxfordSpringer Verlag2015Wathen, AZhu, SThis paper focuses on spectral distribution of kernel matrices related to radial basis functions. By relating a contemporary finite-dimensional linear algebra problem to a classical problem on infinite-dimensional linear integral operator, the paper shows how the spectral distribution of a kernel matrix relates to the smoothness of the underlying kernel function. The asymptotic behaviour of the eigenvalues of a infinite-dimensional kernel operator are studied from a perspective of low rank approximation—approximating an integral operator in terms of Fourier series or Chebyshev series truncations. Further, we study how the spectral distribution of interpolation matrices of an infinite smooth kernel with flat limit depends on the geometric property of the underlying interpolation points. In particularly, the paper discusses the analytic eigenvalue distribution of Gaussian kernels, which has important application on stably computing of Gaussian radial basis functions. |
| spellingShingle | Wathen, A Zhu, S On spectral distribution of kernel matrices related to radial basis functions |
| title | On spectral distribution of kernel matrices related to radial basis functions |
| title_full | On spectral distribution of kernel matrices related to radial basis functions |
| title_fullStr | On spectral distribution of kernel matrices related to radial basis functions |
| title_full_unstemmed | On spectral distribution of kernel matrices related to radial basis functions |
| title_short | On spectral distribution of kernel matrices related to radial basis functions |
| title_sort | on spectral distribution of kernel matrices related to radial basis functions |
| work_keys_str_mv | AT wathena onspectraldistributionofkernelmatricesrelatedtoradialbasisfunctions AT zhus onspectraldistributionofkernelmatricesrelatedtoradialbasisfunctions |