Asharabi, Rashad M.; Prestin, Jurgen Accurate sampling formula for approximating the partial derivatives of bivariate analytic functions. (English) Zbl 1460.94030 Numer. Algorithms 86, No. 4, 1421-1441 (2021). 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. Cited in 1 ReviewCited in 1 Document 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 Keywords:sinc approximation; entire functions of several variables; error bounds; approximating partial derivatives Citations:Zbl 1433.94047 PDFBibTeX XMLCite \textit{R. M. Asharabi} and \textit{J. Prestin}, Numer. Algorithms 86, No. 4, 1421--1441 (2021; Zbl 1460.94030) Full Text: DOI References: [1] Ahlfors, L. V.: Complex Analysis, 3rd ed. McGraw Hill, New York (1979) · Zbl 0395.30001 [2] Annaby, MH, Multivariate sampling theorems associated with multiparameter differential operators, Proc. Edin. Math. Soc., 48, 257-277 (2005) · Zbl 1079.94008 [3] Asharabi, R.M.: Generalized bivariate Hermite-Gauss sampling. Comput. Appl. Math. 38. doi:10.1007/s40314-019-0802-z (2019) · Zbl 1438.94045 [4] Asharabi, RM, The use of the sinc-Gaussian sampling formula for approximating the derivatives of analytic functions, Numer. Algor., 81, 293-312 (2019) · Zbl 1418.30033 [5] Asharabi, RM, Generalized sinc-Gaussian sampling involving derivatives, Numer. Algor., 73, 1055-1072 (2016) · Zbl 1356.30024 [6] Asharabi, RM; Al-Hayzea, AM, Double sampling derivatives and truncation error estimates, Appl. Math. J. Chinese Univ., 33, 209-224 (2018) · Zbl 1399.30091 [7] Asharabi, RM; Prestin, J., A modification of Hermite sampling with a Gaussian multiplier, Numer. Funct. Anal. Optim., 36, 419-437 (2015) · Zbl 1318.30055 [8] Asharabi, RM; Prestin, J., On two-dimensional classical and Hermite sampling, IMA J. Numer. Anal., 36, 851-871 (2016) · Zbl 1433.94047 [9] Gosselin, RP, On the lp theory of cardinal series, Ann. Math., 78, 567-581 (1963) · Zbl 0115.05801 [10] Nikol’skii, S. N.: Approximation of Functions of Several Variables and Imbedding Theorems. Springer, New York (1975) [11] Parzen, E.: A simple proof and some extensions of sampling theorems. Technical Report 7 Stanford University, California, pp. 1-9 (1956) [12] Peterson, DP; Middleton, D., Sampling and reconstruction of wave number-limited functions in N-dimensional Euclidean space, Inform. Control, 5, 279-323 (1962) [13] Qian, L., On the regularized Whittaker-Kotel’nikov-Shannon sampling formula, Proc. Amer. Math. Soc., 131, 1169-1176 (2002) · Zbl 1018.94004 [14] Qian, L.; Creamer, DB, A modification of the sampling series with a Gaussian multiplier, Sampl Theory Signal Image Process, 5, 1-19 (2006) · Zbl 1137.41355 [15] Qian, L.; Creamer, DB, Localized sampling in the presence of noise, Appl. Math. Lett., 19, 351-355 (2006) · Zbl 1095.41020 [16] Schmeisser, G.; Stenger, F., Sinc approximation with a Gaussian multiplier, Sampl. Theory Signal Image Process., 6, 199-221 (2007) · Zbl 1156.94326 [17] Tanaka, K.; Sugihara, M.; Murota, K., Complex analytic approach to the sinc-Gauss sampling formula, J.pan J. Ind. Appl. Math., 25, 209-231 (2008) · Zbl 1152.65123 [18] Vladimirov, VS, Methods of the Theory of Functions of Many Complex Variables (1966), Cambridge: MIT Press, Cambridge This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.