Dissertation/Thesis
On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms
| Τίτλος: | On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms |
|---|---|
| Συγγραφείς: | Erich Kaltofen, Zhengfeng Yang |
| Συνεισφορές: | The Pennsylvania State University CiteSeerX Archives |
| Πηγή: | http://www4.ncsu.edu/~kaltofen/bibliography/07/KYZ07.pdf. |
| Στοιχεία εκδότη: | ACM Press |
| Έτος έκδοσης: | 2007 |
| Συλλογή: | CiteSeerX |
| Θεματικοί όροι: | Categories and Subject Descriptors, I.2.1 [Computing Methodologies, Symbolic and Algebraic Manipulation —Algorithms, G.1.2 [Mathematics of Computing, Numerical Analysis—Approximation General Terms, algorithms, theory, experimentation Keywords, multivariate rational function, interpolation, sparse polynomial |
| Περιγραφή: | Algebraic randomization techniques can be applied to hybrid symbolic-numeric algorithms. Here we consider the problem of interpolating a sparse rational function from noisy values. We develop a new hybrid algorithm based on Zippel’s original sparse polynomial interpolation technique. We show experimentally that our algorithm can handle sparse polynomials with large degrees. We also give a (partial) mathematical justification why the Zippel’s algebraic randomization technique can be used with our approximate data: the randomly generated non-zero values are expected to be bounded away from zero. We show that the random Fourier-like matrices arising in our algorithm, have the desired rank property in the exact case, and appear usable numerically. Furthermore, we show that Sylvester matrices of polynomials with nonidentically distributed random coefficients have large condition numbers. That phenomenon has precluded several algebraic randomization techniques from use in the approximate hybrid setting. |
| Τύπος εγγράφου: | Thesis |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Relation: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.5812; http://www4.ncsu.edu/~kaltofen/bibliography/07/KYZ07.pdf |
| Διαθεσιμότητα: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.5812 http://www4.ncsu.edu/~kaltofen/bibliography/07/KYZ07.pdf |
| Rights: | Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| Αριθμός Καταχώρησης: | edsbas.5136583 |
| Βάση Δεδομένων: | BASE |
| FullText | Text: Availability: 0 CustomLinks: – Url: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.5812# Name: EDS - BASE (ns324271) Category: fullText Text: View record from BASE |
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| Header | DbId: edsbas DbLabel: BASE An: edsbas.5136583 RelevancyScore: 759 AccessLevel: 3 PubType: Dissertation/Thesis PubTypeId: unknown PreciseRelevancyScore: 759.334350585938 |
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| Items | – Name: Title Label: Title Group: Ti Data: On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Erich+Kaltofen%22">Erich Kaltofen</searchLink><br /><searchLink fieldCode="AR" term="%22Zhengfeng+Yang%22">Zhengfeng Yang</searchLink> – Name: Author Label: Contributors Group: Au Data: The Pennsylvania State University CiteSeerX Archives – Name: TitleSource Label: Source Group: Src Data: <i>http://www4.ncsu.edu/~kaltofen/bibliography/07/KYZ07.pdf</i>. – Name: Publisher Label: Publisher Information Group: PubInfo Data: ACM Press – Name: DatePubCY Label: Publication Year Group: Date Data: 2007 – Name: Subset Label: Collection Group: HoldingsInfo Data: CiteSeerX – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Categories+and+Subject+Descriptors%22">Categories and Subject Descriptors</searchLink><br /><searchLink fieldCode="DE" term="%22I%2E2%2E1+[Computing+Methodologies%22">I.2.1 [Computing Methodologies</searchLink><br /><searchLink fieldCode="DE" term="%22Symbolic+and+Algebraic+Manipulation+—Algorithms%22">Symbolic and Algebraic Manipulation —Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22G%2E1%2E2+[Mathematics+of+Computing%22">G.1.2 [Mathematics of Computing</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+Analysis—Approximation+General+Terms%22">Numerical Analysis—Approximation General Terms</searchLink><br /><searchLink fieldCode="DE" term="%22algorithms%22">algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22theory%22">theory</searchLink><br /><searchLink fieldCode="DE" term="%22experimentation+Keywords%22">experimentation Keywords</searchLink><br /><searchLink fieldCode="DE" term="%22multivariate+rational+function%22">multivariate rational function</searchLink><br /><searchLink fieldCode="DE" term="%22interpolation%22">interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22sparse+polynomial%22">sparse polynomial</searchLink> – Name: Abstract Label: Description Group: Ab Data: Algebraic randomization techniques can be applied to hybrid symbolic-numeric algorithms. Here we consider the problem of interpolating a sparse rational function from noisy values. We develop a new hybrid algorithm based on Zippel’s original sparse polynomial interpolation technique. We show experimentally that our algorithm can handle sparse polynomials with large degrees. We also give a (partial) mathematical justification why the Zippel’s algebraic randomization technique can be used with our approximate data: the randomly generated non-zero values are expected to be bounded away from zero. We show that the random Fourier-like matrices arising in our algorithm, have the desired rank property in the exact case, and appear usable numerically. Furthermore, we show that Sylvester matrices of polynomials with nonidentically distributed random coefficients have large condition numbers. That phenomenon has precluded several algebraic randomization techniques from use in the approximate hybrid setting. – Name: TypeDocument Label: Document Type Group: TypDoc Data: Thesis – Name: Format Label: File Description Group: SrcInfo Data: application/pdf – Name: Language Label: Language Group: Lang Data: English – Name: NoteTitleSource Label: Relation Group: SrcInfo Data: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.5812; http://www4.ncsu.edu/~kaltofen/bibliography/07/KYZ07.pdf – Name: URL Label: Availability Group: URL Data: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.5812<br />http://www4.ncsu.edu/~kaltofen/bibliography/07/KYZ07.pdf – Name: Copyright Label: Rights Group: Cpyrght Data: Metadata may be used without restrictions as long as the oai identifier remains attached to it. – Name: AN Label: Accession Number Group: ID Data: edsbas.5136583 |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.5136583 |
| RecordInfo | BibRecord: BibEntity: Languages: – Text: English Subjects: – SubjectFull: Categories and Subject Descriptors Type: general – SubjectFull: I.2.1 [Computing Methodologies Type: general – SubjectFull: Symbolic and Algebraic Manipulation —Algorithms Type: general – SubjectFull: G.1.2 [Mathematics of Computing Type: general – SubjectFull: Numerical Analysis—Approximation General Terms Type: general – SubjectFull: algorithms Type: general – SubjectFull: theory Type: general – SubjectFull: experimentation Keywords Type: general – SubjectFull: multivariate rational function Type: general – SubjectFull: interpolation Type: general – SubjectFull: sparse polynomial Type: general Titles: – TitleFull: On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Erich Kaltofen – PersonEntity: Name: NameFull: Zhengfeng Yang – PersonEntity: Name: NameFull: The Pennsylvania State University CiteSeerX Archives IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2007 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa Titles: – TitleFull: http://www4.ncsu.edu/~kaltofen/bibliography/07/KYZ07.pdf Type: main |
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