Vandermonde with Arnoldi
Vandermonde matrices are exponentially ill-conditioned, rendering the familiar “polyval(polyfit)” algorithm for polynomial interpolation and least-squares fitting ineffective at higher degrees. We show that Arnoldi orthogonalization fixes the problem. This amounts to on-the-fly construction of discr...
| Main Authors: | , , |
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| Formato: | Journal article |
| Idioma: | English |
| Publicado em: |
Society for Industrial and Applied Mathematics
2021
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| _version_ | 1826284846640529408 |
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| author | Brubeck, PD Nakatsukasa, Y Trefethen, LN |
| author_facet | Brubeck, PD Nakatsukasa, Y Trefethen, LN |
| author_sort | Brubeck, PD |
| collection | OXFORD |
| description | Vandermonde matrices are exponentially ill-conditioned, rendering the familiar “polyval(polyfit)” algorithm for polynomial interpolation and least-squares fitting ineffective at higher degrees. We show that Arnoldi orthogonalization fixes the problem. This amounts to on-the-fly construction of discrete orthogonal polynomials by Stieltjes orthogonalization. |
| first_indexed | 2024-03-07T01:19:58Z |
| format | Journal article |
| id | oxford-uuid:8ffd5cfd-98c8-4bfe-80c2-1cf781daf4a9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:19:58Z |
| publishDate | 2021 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:8ffd5cfd-98c8-4bfe-80c2-1cf781daf4a92022-03-26T23:08:33ZVandermonde with ArnoldiJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8ffd5cfd-98c8-4bfe-80c2-1cf781daf4a9EnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2021Brubeck, PDNakatsukasa, YTrefethen, LNVandermonde matrices are exponentially ill-conditioned, rendering the familiar “polyval(polyfit)” algorithm for polynomial interpolation and least-squares fitting ineffective at higher degrees. We show that Arnoldi orthogonalization fixes the problem. This amounts to on-the-fly construction of discrete orthogonal polynomials by Stieltjes orthogonalization. |
| spellingShingle | Brubeck, PD Nakatsukasa, Y Trefethen, LN Vandermonde with Arnoldi |
| title | Vandermonde with Arnoldi |
| title_full | Vandermonde with Arnoldi |
| title_fullStr | Vandermonde with Arnoldi |
| title_full_unstemmed | Vandermonde with Arnoldi |
| title_short | Vandermonde with Arnoldi |
| title_sort | vandermonde with arnoldi |
| work_keys_str_mv | AT brubeckpd vandermondewitharnoldi AT nakatsukasay vandermondewitharnoldi AT trefethenln vandermondewitharnoldi |