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Uniqueness of solutions in multivariate Chebyshev approximation problems

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Název: Uniqueness of solutions in multivariate Chebyshev approximation problems
Autoři: Vera Roshchina, Nadezda Sukhorukova, Julien Ugon
Rok vydání: 2024
Témata: Mathematical sciences, Applied mathematics, Numerical and computational mathematics, Pure mathematics, ALGORITHM, Chebyshev approximation, Mathematics, Applied, Multivariate polynomial approximation, Operations Research & Management Science, Physical Sciences, Science & Technology, Technology, Uniqueness of solutions
Popis: We study the solution set to multivariate Chebyshev approximation problem, focussing on the ill-posed case when the uniqueness of solutions can not be established via strict polynomial separation. We obtain an upper bound on the dimension of the solution set and show that nonuniqueness is generic for ill-posed problems on discrete domains. Moreover, given a prescribed set of points of minimal and maximal deviation we construct a function for which the dimension of the set of best approximating polynomials is maximal for any choice of domain. We also present several examples that illustrate the aforementioned phenomena, demonstrate practical application of our results and propose a number of open questions.
Druh dokumentu: article in journal/newspaper
Jazyk: unknown
Relation: http://hdl.handle.net/10779/DRO/DU:24165987.v1; https://figshare.com/articles/journal_contribution/Uniqueness_of_solutions_in_multivariate_Chebyshev_approximation_problems/24165987
Dostupnost: http://hdl.handle.net/10779/DRO/DU:24165987.v1
https://figshare.com/articles/journal_contribution/Uniqueness_of_solutions_in_multivariate_Chebyshev_approximation_problems/24165987
Rights: All Rights Reserved
Přístupové číslo: edsbas.5113E271
Databáze: BASE
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  – Url: http://hdl.handle.net/10779/DRO/DU:24165987.v1#
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Items – Name: Title
  Label: Title
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  Data: Uniqueness of solutions in multivariate Chebyshev approximation problems
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Vera+Roshchina%22">Vera Roshchina</searchLink><br /><searchLink fieldCode="AR" term="%22Nadezda+Sukhorukova%22">Nadezda Sukhorukova</searchLink><br /><searchLink fieldCode="AR" term="%22Julien+Ugon%22">Julien Ugon</searchLink>
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2024
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Mathematical+sciences%22">Mathematical sciences</searchLink><br /><searchLink fieldCode="DE" term="%22Applied+mathematics%22">Applied mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+and+computational+mathematics%22">Numerical and computational mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Pure+mathematics%22">Pure mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22ALGORITHM%22">ALGORITHM</searchLink><br /><searchLink fieldCode="DE" term="%22Chebyshev+approximation%22">Chebyshev approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Applied%22">Applied</searchLink><br /><searchLink fieldCode="DE" term="%22Multivariate+polynomial+approximation%22">Multivariate polynomial approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Operations+Research+%26+Management+Science%22">Operations Research & Management Science</searchLink><br /><searchLink fieldCode="DE" term="%22Physical+Sciences%22">Physical Sciences</searchLink><br /><searchLink fieldCode="DE" term="%22Science+%26+Technology%22">Science & Technology</searchLink><br /><searchLink fieldCode="DE" term="%22Technology%22">Technology</searchLink><br /><searchLink fieldCode="DE" term="%22Uniqueness+of+solutions%22">Uniqueness of solutions</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: We study the solution set to multivariate Chebyshev approximation problem, focussing on the ill-posed case when the uniqueness of solutions can not be established via strict polynomial separation. We obtain an upper bound on the dimension of the solution set and show that nonuniqueness is generic for ill-posed problems on discrete domains. Moreover, given a prescribed set of points of minimal and maximal deviation we construct a function for which the dimension of the set of best approximating polynomials is maximal for any choice of domain. We also present several examples that illustrate the aforementioned phenomena, demonstrate practical application of our results and propose a number of open questions.
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  Data: article in journal/newspaper
– Name: Language
  Label: Language
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  Data: unknown
– Name: NoteTitleSource
  Label: Relation
  Group: SrcInfo
  Data: http://hdl.handle.net/10779/DRO/DU:24165987.v1; https://figshare.com/articles/journal_contribution/Uniqueness_of_solutions_in_multivariate_Chebyshev_approximation_problems/24165987
– Name: URL
  Label: Availability
  Group: URL
  Data: http://hdl.handle.net/10779/DRO/DU:24165987.v1<br />https://figshare.com/articles/journal_contribution/Uniqueness_of_solutions_in_multivariate_Chebyshev_approximation_problems/24165987
– Name: Copyright
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  Data: All Rights Reserved
– Name: AN
  Label: Accession Number
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  Data: edsbas.5113E271
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RecordInfo BibRecord:
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      – Text: unknown
    Subjects:
      – SubjectFull: Mathematical sciences
        Type: general
      – SubjectFull: Applied mathematics
        Type: general
      – SubjectFull: Numerical and computational mathematics
        Type: general
      – SubjectFull: Pure mathematics
        Type: general
      – SubjectFull: ALGORITHM
        Type: general
      – SubjectFull: Chebyshev approximation
        Type: general
      – SubjectFull: Mathematics
        Type: general
      – SubjectFull: Applied
        Type: general
      – SubjectFull: Multivariate polynomial approximation
        Type: general
      – SubjectFull: Operations Research & Management Science
        Type: general
      – SubjectFull: Physical Sciences
        Type: general
      – SubjectFull: Science & Technology
        Type: general
      – SubjectFull: Technology
        Type: general
      – SubjectFull: Uniqueness of solutions
        Type: general
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      – TitleFull: Uniqueness of solutions in multivariate Chebyshev approximation problems
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          Name:
            NameFull: Vera Roshchina
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            NameFull: Nadezda Sukhorukova
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            NameFull: Julien Ugon
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            – D: 01
              M: 01
              Type: published
              Y: 2024
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