A robust implementation of the Carath,odory-Fej,r method for rational approximation
Best rational approximations are notoriously difficult to compute. However, the difference between the best rational approximation to a function and its Carathéodory-Fejér (CF) approximation is often so small as to be negligible in practice, while CF approximations are far easier to compute. We pres...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2011
|
| _version_ | 1797098177033142272 |
|---|---|
| author | Van Deun, J Trefethen, L |
| author_facet | Van Deun, J Trefethen, L |
| author_sort | Van Deun, J |
| collection | OXFORD |
| description | Best rational approximations are notoriously difficult to compute. However, the difference between the best rational approximation to a function and its Carathéodory-Fejér (CF) approximation is often so small as to be negligible in practice, while CF approximations are far easier to compute. We present a robust and fast implementation of this method in the Chebfun software system and illustrate its use with several examples. Our implementation handles both polynomial and rational approximation and substantially improves upon earlier published software. © 2011 Springer Science + Business Media B.V. |
| first_indexed | 2024-03-07T05:05:52Z |
| format | Journal article |
| id | oxford-uuid:d9e4cf53-e344-4e59-8de4-4348f9c7aee6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:05:52Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:d9e4cf53-e344-4e59-8de4-4348f9c7aee62022-03-27T08:59:15ZA robust implementation of the Carath,odory-Fej,r method for rational approximationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d9e4cf53-e344-4e59-8de4-4348f9c7aee6EnglishSymplectic Elements at Oxford2011Van Deun, JTrefethen, LBest rational approximations are notoriously difficult to compute. However, the difference between the best rational approximation to a function and its Carathéodory-Fejér (CF) approximation is often so small as to be negligible in practice, while CF approximations are far easier to compute. We present a robust and fast implementation of this method in the Chebfun software system and illustrate its use with several examples. Our implementation handles both polynomial and rational approximation and substantially improves upon earlier published software. © 2011 Springer Science + Business Media B.V. |
| spellingShingle | Van Deun, J Trefethen, L A robust implementation of the Carath,odory-Fej,r method for rational approximation |
| title | A robust implementation of the Carath,odory-Fej,r method for rational approximation |
| title_full | A robust implementation of the Carath,odory-Fej,r method for rational approximation |
| title_fullStr | A robust implementation of the Carath,odory-Fej,r method for rational approximation |
| title_full_unstemmed | A robust implementation of the Carath,odory-Fej,r method for rational approximation |
| title_short | A robust implementation of the Carath,odory-Fej,r method for rational approximation |
| title_sort | robust implementation of the carath odory fej r method for rational approximation |
| work_keys_str_mv | AT vandeunj arobustimplementationofthecarathodoryfejrmethodforrationalapproximation AT trefethenl arobustimplementationofthecarathodoryfejrmethodforrationalapproximation AT vandeunj robustimplementationofthecarathodoryfejrmethodforrationalapproximation AT trefethenl robustimplementationofthecarathodoryfejrmethodforrationalapproximation |