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Accurate sampling formula for approximating the partial derivatives of bivariate analytic functions. (English) Zbl 1460.94030

Summary: The bivariate sinc-Gauss sampling formula is introduced in R. M. Asharabi and J. Prestin [IMA J. Numer. Anal. 36, No. 2, 851–871 (2016; Zbl 1433.94047)] to approximate analytic functions of two variables which satisfy certain growth condition. In this paper, we apply this formula to approximate partial derivatives of any order for entire and holomorphic functions on an infinite horizontal strip domain using only finitely many samples of the function itself. The rigorous error analysis is carried out with sharp estimates based on a complex analytic approach. The convergence rate of this technique will be of exponential type, and it has a high accuracy in comparison with the accuracy of the bivariate classical sampling formula. Several computational examples are exhibited, demonstrating the exactness of the obtained results.

MSC:

94A20 Sampling theory in information and communication theory
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
32A15 Entire functions of several complex variables
41A80 Remainders in approximation formulas
41A25 Rate of convergence, degree of approximation
65L70 Error bounds for numerical methods for ordinary differential equations

Citations:

Zbl 1433.94047
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References:

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