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Chebyshev Multivariate Polynomial Approximation and Point Reduction Procedure.

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Název: Chebyshev Multivariate Polynomial Approximation and Point Reduction Procedure.
Autoři: Sukhorukova, Nadezda, Ugon, Julien, Yost, David
Zdroj: Constructive Approximation; Jun2021, Vol. 53 Issue 3, p529-544, 16p
Témata: POLYNOMIAL approximation, CHEBYSHEV polynomials, CHEBYSHEV approximation, POLYNOMIALS, NONSMOOTH optimization
Abstrakt: We apply the methods of nonsmooth and convex analysis to extend the study of Chebyshev (uniform) approximation for univariate polynomial functions to the case of general multivariate functions (not just polynomials). First of all, we give new necessary and sufficient optimality conditions for multivariate approximation, and a geometrical interpretation of them which reduces to the classical alternating sequence condition in the univariate case. Then, we present a procedure for verification of necessary and sufficient optimality conditions that is based on our generalization of the notion of alternating sequence to the case of multivariate polynomials. Finally, we develop an algorithm for fast verification of necessary optimality conditions in the multivariate polynomial case. [ABSTRACT FROM AUTHOR]
Copyright of Constructive Approximation is the property of Springer Nature 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.)
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  Data: Chebyshev Multivariate Polynomial Approximation and Point Reduction Procedure.
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  Data: Constructive Approximation; Jun2021, Vol. 53 Issue 3, p529-544, 16p
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  Data: <searchLink fieldCode="DE" term="%22POLYNOMIAL+approximation%22">POLYNOMIAL approximation</searchLink><br /><searchLink fieldCode="DE" term="%22CHEBYSHEV+polynomials%22">CHEBYSHEV polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22CHEBYSHEV+approximation%22">CHEBYSHEV approximation</searchLink><br /><searchLink fieldCode="DE" term="%22POLYNOMIALS%22">POLYNOMIALS</searchLink><br /><searchLink fieldCode="DE" term="%22NONSMOOTH+optimization%22">NONSMOOTH optimization</searchLink>
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  Label: Abstract
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  Data: We apply the methods of nonsmooth and convex analysis to extend the study of Chebyshev (uniform) approximation for univariate polynomial functions to the case of general multivariate functions (not just polynomials). First of all, we give new necessary and sufficient optimality conditions for multivariate approximation, and a geometrical interpretation of them which reduces to the classical alternating sequence condition in the univariate case. Then, we present a procedure for verification of necessary and sufficient optimality conditions that is based on our generalization of the notion of alternating sequence to the case of multivariate polynomials. Finally, we develop an algorithm for fast verification of necessary optimality conditions in the multivariate polynomial case. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Constructive Approximation is the property of Springer Nature 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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      – SubjectFull: CHEBYSHEV polynomials
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      – SubjectFull: NONSMOOTH optimization
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      – TitleFull: Chebyshev Multivariate Polynomial Approximation and Point Reduction Procedure.
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              Text: Jun2021
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