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

Y.V. Semenova and S.G. Solodky

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PA, 1-14

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 L2-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.

Keywords: Numerical differentiation; Self-regularization; Truncation method; Hyperbolic cross; Legendre polynomials; Information complexity; Optimal error estimates (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pa:p:1-14

DOI: 10.1016/j.matcom.2025.08.020

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