An approximation of analytical functions by local splines |
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Authors: | Ilya V. Boikov |
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Affiliation: | (1) Departmant of Mathematics, Penza State Technical University, 440017 Penza, Russia |
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Abstract: | Local splines are presented for the approximation of functions of one and many variables, which are analytic in the domains , where Ui(zi) is a unit disk in the complex plane Ci,i=1,2,…,l, l=1,2, …. Results are given for functions whose r-order derivatives belong to the Hardy's class Hp,1≤p≤∞. It is shown that the approximation converge to the function at the rate for functions of one variable and An−(r−1/p)/(l−1) for functions of l variables, where n is the number of points of local splines and A and C are positive constants. This work was supported by Russian Foundation of Fundumental Inverstigations |
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