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On self-regularization for the recovery of high order partial derivatives of bivariate functions.

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Title: On self-regularization for the recovery of high order partial derivatives of bivariate functions.
Authors: Semenova, Y.V.1 (AUTHOR) semenovaevgen@gmail.com, Solodky, S.G.1,2 (AUTHOR) solodky@imath.kiev.ua
Source: Mathematics & Computers in Simulation. Mar2026:Part A, Vol. 241, p1-14. 14p.
Subjects: High-order derivatives (Mathematics), Numerical differentiation, Multivariable calculus, Empirical research, Iterative methods (Mathematics), Mathematical regularization, Approximation error
Abstract: This paper studies the efficient recovery of high-order partial derivatives of bivariate functions from noisy data. Based on the principle of self-regularization, we construct a version of the truncation method. The error of the proposed numerical differentiation algorithm is estimated in uniform and L 2 -metrics. We establish that this approach achieves order-optimal error estimates with respect to accuracy and the amount of discrete information involved. Numerical demonstrations are given to illustrate that the proposed method can be successfully implemented. [ABSTRACT FROM AUTHOR]
Copyright of Mathematics & Computers in Simulation 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.)
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DbLabel: Engineering Source
An: 189765152
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  Data: This paper studies the efficient recovery of high-order partial derivatives of bivariate functions from noisy data. Based on the principle of self-regularization, we construct a version of the truncation method. The error of the proposed numerical differentiation algorithm is estimated in uniform and L 2 -metrics. We establish that this approach achieves order-optimal error estimates with respect to accuracy and the amount of discrete information involved. Numerical demonstrations are given to illustrate that the proposed method can be successfully implemented. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Mathematics & Computers in Simulation 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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      – Type: doi
        Value: 10.1016/j.matcom.2025.08.020
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      – Code: eng
        Text: English
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        PageCount: 14
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    Subjects:
      – SubjectFull: High-order derivatives (Mathematics)
        Type: general
      – SubjectFull: Numerical differentiation
        Type: general
      – SubjectFull: Multivariable calculus
        Type: general
      – SubjectFull: Empirical research
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Mathematical regularization
        Type: general
      – SubjectFull: Approximation error
        Type: general
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      – TitleFull: On self-regularization for the recovery of high order partial derivatives of bivariate functions.
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              M: 03
              Text: Mar2026:Part A
              Type: published
              Y: 2026
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