View in EDS PDF Full Text

A Sum of Squares Approximation of Nonnegative Polynomials.

Saved in:
Bibliographic Details
Title: A Sum of Squares Approximation of Nonnegative Polynomials.
Authors: Lasserre, Jean B.1 lasserre@laas.fr
Source: SIAM Journal on Optimization. 2006, Vol. 16 Issue 3, p751-765. 15p.
Subjects: Polynomials, EPSILON (Computer program language), Nonnegative matrices, Vector analysis, Algebra
Abstract: We show that every real nonnegative polynomial $f$ can be approximated as closely as desired (in the $l_1$-norm of its coefficient vector) by a sequence of polynomials $\{f_\epsilon\}$ that are sums of squares. The novelty is that each $f_\epsilon$ has a simple and explicit form in terms of $f$ and $\epsilon$. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Optimization 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 Links:
  – Type: pdflink
Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 19527818
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: A Sum of Squares Approximation of Nonnegative Polynomials.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Lasserre%2C+Jean+B%2E%22">Lasserre, Jean B.</searchLink><relatesTo>1</relatesTo><i> lasserre@laas.fr</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Optimization%22">SIAM Journal on Optimization</searchLink>. 2006, Vol. 16 Issue 3, p751-765. 15p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22EPSILON+%28Computer+program+language%29%22">EPSILON (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Nonnegative+matrices%22">Nonnegative matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+analysis%22">Vector analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We show that every real nonnegative polynomial $f$ can be approximated as closely as desired (in the $l_1$-norm of its coefficient vector) by a sequence of polynomials $\{f_\epsilon\}$ that are sums of squares. The novelty is that each $f_\epsilon$ has a simple and explicit form in terms of $f$ and $\epsilon$. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of SIAM Journal on Optimization 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=19527818
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1137/04061413X
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 751
    Subjects:
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: EPSILON (Computer program language)
        Type: general
      – SubjectFull: Nonnegative matrices
        Type: general
      – SubjectFull: Vector analysis
        Type: general
      – SubjectFull: Algebra
        Type: general
    Titles:
      – TitleFull: A Sum of Squares Approximation of Nonnegative Polynomials.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Lasserre, Jean B.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 28
              M: 01
              Text: 2006
              Type: published
              Y: 2006
          Identifiers:
            – Type: issn-print
              Value: 10526234
          Numbering:
            – Type: volume
              Value: 16
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: SIAM Journal on Optimization
              Type: main
ResultId 1