Simple varieties for limited precision points.
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| Title: | Simple varieties for limited precision points. |
|---|---|
| Authors: | Fassino, Claudia1 fassino@dima.unige.it, Torrente, Maria-Laura1 torrente@dima.unige.it |
| Source: | Theoretical Computer Science. Apr2013, Vol. 479, p174-186. 13p. |
| Subjects: | Precision (Information retrieval), Set theory, Finite element method, Numerical analysis, Combinatorics, Algebra software |
| Abstract: | Abstract: Given a finite set of points and a tolerance representing the maximum error on the coordinates of each point, we address the problem of computing a simple polynomial whose zero-locus “almost” contains the points of . We propose a symbolic–numerical method that, starting from the knowledge of and , determines a polynomial whose degree is strictly bounded by the minimal degree of the elements of the vanishing ideal of . Then, in Theorem 4.3, we state the sufficient conditions for proving that lies close to each point of by less than . The validity of the proposed method relies on a combination of classical results of Computer Algebra and Numerical Analysis; its effectiveness is illustrated with a number of examples. [Copyright &y& Elsevier] |
| Copyright of Theoretical Computer Science is the property of Elsevier B.V. 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: 89478365 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Simple varieties for limited precision points. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Fassino%2C+Claudia%22">Fassino, Claudia</searchLink><relatesTo>1</relatesTo><i> fassino@dima.unige.it</i><br /><searchLink fieldCode="AR" term="%22Torrente%2C+Maria-Laura%22">Torrente, Maria-Laura</searchLink><relatesTo>1</relatesTo><i> torrente@dima.unige.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+Computer+Science%22">Theoretical Computer Science</searchLink>. Apr2013, Vol. 479, p174-186. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Precision+%28Information+retrieval%29%22">Precision (Information retrieval)</searchLink><br /><searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra+software%22">Algebra software</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: Given a finite set of points and a tolerance representing the maximum error on the coordinates of each point, we address the problem of computing a simple polynomial whose zero-locus “almost” contains the points of . We propose a symbolic–numerical method that, starting from the knowledge of and , determines a polynomial whose degree is strictly bounded by the minimal degree of the elements of the vanishing ideal of . Then, in Theorem 4.3, we state the sufficient conditions for proving that lies close to each point of by less than . The validity of the proposed method relies on a combination of classical results of Computer Algebra and Numerical Analysis; its effectiveness is illustrated with a number of examples. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Theoretical Computer Science is the property of Elsevier B.V. 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: 10.1016/j.tcs.2012.10.024 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 174 Subjects: – SubjectFull: Precision (Information retrieval) Type: general – SubjectFull: Set theory Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Combinatorics Type: general – SubjectFull: Algebra software Type: general Titles: – TitleFull: Simple varieties for limited precision points. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Fassino, Claudia – PersonEntity: Name: NameFull: Torrente, Maria-Laura IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2013 Type: published Y: 2013 Identifiers: – Type: issn-print Value: 03043975 Numbering: – Type: volume Value: 479 Titles: – TitleFull: Theoretical Computer Science Type: main |
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