Impossibility of approximating analytic functions from equispaced samples
It is shown that no stable procedure for approximating functions from equally spaced samples can converge geometrically for analytic functions. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992.
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| Format: | Report |
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SIAM Review
2009
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| _version_ | 1797081537129218048 |
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| author | Platte, R Trefethen, L Kuijlaars, A |
| author_facet | Platte, R Trefethen, L Kuijlaars, A |
| author_sort | Platte, R |
| collection | OXFORD |
| description | It is shown that no stable procedure for approximating functions from equally spaced samples can converge geometrically for analytic functions. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992. |
| first_indexed | 2024-03-07T01:15:38Z |
| format | Report |
| id | oxford-uuid:8e8fa82b-d508-4f3c-91cd-515d56ddc560 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:15:38Z |
| publishDate | 2009 |
| publisher | SIAM Review |
| record_format | dspace |
| spelling | oxford-uuid:8e8fa82b-d508-4f3c-91cd-515d56ddc5602022-03-26T22:58:35ZImpossibility of approximating analytic functions from equispaced samplesReporthttp://purl.org/coar/resource_type/c_93fcuuid:8e8fa82b-d508-4f3c-91cd-515d56ddc560Mathematical Institute - ePrintsSIAM Review2009Platte, RTrefethen, LKuijlaars, AIt is shown that no stable procedure for approximating functions from equally spaced samples can converge geometrically for analytic functions. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992. |
| spellingShingle | Platte, R Trefethen, L Kuijlaars, A Impossibility of approximating analytic functions from equispaced samples |
| title | Impossibility of approximating analytic functions from equispaced samples |
| title_full | Impossibility of approximating analytic functions from equispaced samples |
| title_fullStr | Impossibility of approximating analytic functions from equispaced samples |
| title_full_unstemmed | Impossibility of approximating analytic functions from equispaced samples |
| title_short | Impossibility of approximating analytic functions from equispaced samples |
| title_sort | impossibility of approximating analytic functions from equispaced samples |
| work_keys_str_mv | AT platter impossibilityofapproximatinganalyticfunctionsfromequispacedsamples AT trefethenl impossibilityofapproximatinganalyticfunctionsfromequispacedsamples AT kuijlaarsa impossibilityofapproximatinganalyticfunctionsfromequispacedsamples |