Abstract
This paper deals with the problem of approximate evaluation of a certain class of analytic functions. The choice of this class is motivated by the problem of the summation of moment sequences. By assuming that the information about the function is given by its Taylor coefficients, we are able to establish a lower bound on the error of an arbitrary algorithm. We present also an algorithm whose error is asymptotically at most twice the lower bound, thereby showing that our estimate is asymptotically sharp.
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Communicated by Charles A. Micchelli.
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Trojan, G.M. Generalized faber polynomials and an optimal error recovery algorithm. Constr. Approx 2, 101–111 (1986). https://doi.org/10.1007/BF01893419
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DOI: https://doi.org/10.1007/BF01893419