Approximation of analytic functions of severalvariables by linear k-positive operators

Coşkun, Tülin

doi:10.3906/mat-1512-96

Turk J Math

2017

DOI: 10.3906/mat-1512-96

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Approximation of analytic functions of severalvariables by linear k-positive operators

Tülin Coşkun¹

Abstract: We investigate the approximation of analytic functions of several variables in polydiscs by the sequences of linear k-positive operators in the Gadjiev sense.

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2019

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Numerical Solution for the Extrapolation Problem of Analytic Functions

Bakas

2019

Research

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In this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude of O(10−100) or less. A variety of integrated radial basis functions are utilized for the solution, as well as variable precision arithmetic for the calculations. Multiple alterations in the function’s direction, with no curvature or periodicity information specified, are efficiently foreseen. Interestingly, the proposed procedure can be extended in multiple dimensions. The attained extrapolation spans are greater than two times the given domain length. The significance of the approximation errors is comprehensively analyzed and reported, for 5832 test cases.

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Numerical Solution for the Extrapolation Problem of Analytic Functions

Bakas

2019

Research

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Approximation of analytic functions of severalvariables by linear k-positive operators

Abstract: We investigate the approximation of analytic functions of several variables in polydiscs by the sequences of linear k-positive operators in the Gadjiev sense.

Cited by 1 publication

References 10 publications

Numerical Solution for the Extrapolation Problem of Analytic Functions

Numerical Solution for the Extrapolation Problem of Analytic Functions

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