FAST POLYNOMIAL TRANSFORMS BASED ON TOEPLITZ AND HANKEL MATRICES.
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| Title: | FAST POLYNOMIAL TRANSFORMS BASED ON TOEPLITZ AND HANKEL MATRICES. |
|---|---|
| Authors: | TOWNSEND, ALEX1 townsend@cornell.edu, WEBB, MARCUS2 marcus.webb@cs.kuleuven.be, OLVER, SHEEHAN s.olver@imperial.ac.uk |
| Source: | Mathematics of Computation. Jul2018, Vol. 37 Issue 312, p1913-1934. 22p. |
| Subjects: | Polynomials, Integral transforms, Toeplitz matrices, Hankel functions, Hadamard matrices |
| Abstract: | Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonallyscaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive algorithms with an observed complexity of O(N log²N), based on the fast Fourier transform, for converting coefficients of a degree N polynomial in one polynomial basis to coefficients in another. Numerical results show that this approach is competitive with state-of-the-art techniques, requires no precomputational cost, can be implemented in a handful of lines of code, and is easily adapted to extended precision arithmetic. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics of Computation is the property of American Mathematical Society 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 129345592 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: FAST POLYNOMIAL TRANSFORMS BASED ON TOEPLITZ AND HANKEL MATRICES. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22TOWNSEND%2C+ALEX%22">TOWNSEND, ALEX</searchLink><relatesTo>1</relatesTo><i> townsend@cornell.edu</i><br /><searchLink fieldCode="AR" term="%22WEBB%2C+MARCUS%22">WEBB, MARCUS</searchLink><relatesTo>2</relatesTo><i> marcus.webb@cs.kuleuven.be</i><br /><searchLink fieldCode="AR" term="%22OLVER%2C+SHEEHAN%22">OLVER, SHEEHAN</searchLink><i> s.olver@imperial.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Computation%22">Mathematics of Computation</searchLink>. Jul2018, Vol. 37 Issue 312, p1913-1934. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+transforms%22">Integral transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Toeplitz+matrices%22">Toeplitz matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Hankel+functions%22">Hankel functions</searchLink><br /><searchLink fieldCode="DE" term="%22Hadamard+matrices%22">Hadamard matrices</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonallyscaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive algorithms with an observed complexity of O(N log²N), based on the fast Fourier transform, for converting coefficients of a degree N polynomial in one polynomial basis to coefficients in another. Numerical results show that this approach is competitive with state-of-the-art techniques, requires no precomputational cost, can be implemented in a handful of lines of code, and is easily adapted to extended precision arithmetic. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics of Computation is the property of American Mathematical Society 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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1090/mcom/3277 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 1913 Subjects: – SubjectFull: Polynomials Type: general – SubjectFull: Integral transforms Type: general – SubjectFull: Toeplitz matrices Type: general – SubjectFull: Hankel functions Type: general – SubjectFull: Hadamard matrices Type: general Titles: – TitleFull: FAST POLYNOMIAL TRANSFORMS BASED ON TOEPLITZ AND HANKEL MATRICES. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: TOWNSEND, ALEX – PersonEntity: Name: NameFull: WEBB, MARCUS – PersonEntity: Name: NameFull: OLVER, SHEEHAN IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 00255718 Numbering: – Type: volume Value: 37 – Type: issue Value: 312 Titles: – TitleFull: Mathematics of Computation Type: main |
| ResultId | 1 |
