STABILITY OF BARYCENTRIC INTERPOLATION FORMULAS FOR EXTRAPOLATION.
Saved in:
| Title: | STABILITY OF BARYCENTRIC INTERPOLATION FORMULAS FOR EXTRAPOLATION. |
|---|---|
| Authors: | WEBB, MARCUS1 m.d.webb@maths.cam.ac.uk, TREFETHEN, LLOYD N.2 trefethen@maths.ox.ac.uk, GONNET, PEDRO3 pedro.gonnet@durham.ac.uk |
| Source: | SIAM Journal on Scientific Computing. 2012, Vol. 34 Issue 6, pA3009-A3015. 7p. |
| Subjects: | Barycentric interpolation, Interpolation, Extrapolation, Approximation theory, Plasma Bernstein waves |
| Abstract: | The barycentric interpolation formula de?nes a stable algorithm for evaluation at points in [-1, 1] of polynomial interpolants through data on Chebyshev grids. Here it is shown that for evaluation at points in the complex plane outside [11], the algorithm becomes unstable and should be replaced by the alternative modified Lagrange or "first barycentric" formula dating to Jacobi in 1825. This difference in stability confirms the theory published by N. J. Higham in 2004 [IMA J. Numer. Anal., 24 (2004), pp. 547-556] and has practical consequences for computation with rational functions. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 87311950 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: STABILITY OF BARYCENTRIC INTERPOLATION FORMULAS FOR EXTRAPOLATION. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22WEBB%2C+MARCUS%22">WEBB, MARCUS</searchLink><relatesTo>1</relatesTo><i> m.d.webb@maths.cam.ac.uk</i><br /><searchLink fieldCode="AR" term="%22TREFETHEN%2C+LLOYD+N%2E%22">TREFETHEN, LLOYD N.</searchLink><relatesTo>2</relatesTo><i> trefethen@maths.ox.ac.uk</i><br /><searchLink fieldCode="AR" term="%22GONNET%2C+PEDRO%22">GONNET, PEDRO</searchLink><relatesTo>3</relatesTo><i> pedro.gonnet@durham.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Scientific+Computing%22">SIAM Journal on Scientific Computing</searchLink>. 2012, Vol. 34 Issue 6, pA3009-A3015. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Barycentric+interpolation%22">Barycentric interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Extrapolation%22">Extrapolation</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Plasma+Bernstein+waves%22">Plasma Bernstein waves</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The barycentric interpolation formula de?nes a stable algorithm for evaluation at points in [-1, 1] of polynomial interpolants through data on Chebyshev grids. Here it is shown that for evaluation at points in the complex plane outside [11], the algorithm becomes unstable and should be replaced by the alternative modified Lagrange or "first barycentric" formula dating to Jacobi in 1825. This difference in stability confirms the theory published by N. J. Higham in 2004 [IMA J. Numer. Anal., 24 (2004), pp. 547-556] and has practical consequences for computation with rational functions. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=87311950 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/110848797 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: A3009 Subjects: – SubjectFull: Barycentric interpolation Type: general – SubjectFull: Interpolation Type: general – SubjectFull: Extrapolation Type: general – SubjectFull: Approximation theory Type: general – SubjectFull: Plasma Bernstein waves Type: general Titles: – TitleFull: STABILITY OF BARYCENTRIC INTERPOLATION FORMULAS FOR EXTRAPOLATION. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: WEBB, MARCUS – PersonEntity: Name: NameFull: TREFETHEN, LLOYD N. – PersonEntity: Name: NameFull: GONNET, PEDRO IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: 2012 Type: published Y: 2012 Identifiers: – Type: issn-print Value: 10648275 Numbering: – Type: volume Value: 34 – Type: issue Value: 6 Titles: – TitleFull: SIAM Journal on Scientific Computing Type: main |
| ResultId | 1 |
