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On a nontraditional method of approximation

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Abstract

We study the approximation of functions f(z) that are analytic in a neighborhood of zero by finite sums of the form H n (z) = H n (h, f, {λ k }; z) = Σ nk=1 λ k h(λ k z), where h is a fixed function that is analytic in the unit disk |z| < 1 and the numbers λ k (which depend on h, f, and n) are calculated by a certain algorithm. An exact value of the radius of the convergence H n (z) → f(z), n → ∞, and an order-sharp estimate for the rate of this convergence are obtained; an application to numerical analysis is given.

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Authors and Affiliations

  1. Chair of Functional Analysis and Its Applications, Vladimir State University, ul. Gor’kogo 87, Vladimir, 600000, Russia

    P. V. Chunaev

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  1. P. V. Chunaev
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Correspondence to P. V. Chunaev.

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Original Russian Text © P.V. Chunaev, 2010, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Vol. 270, pp. 281–287.

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Chunaev, P.V. On a nontraditional method of approximation. Proc. Steklov Inst. Math. 270, 278–284 (2010). https://doi.org/10.1134/S0081543810030223

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