Best approximation of positive power series

Author:
B. L. R. Shawyer

Journal:
Math. Comp. **43** (1984), 529-534

MSC:
Primary 41A10; Secondary 41A50

DOI:
https://doi.org/10.1090/S0025-5718-1984-0758199-2

MathSciNet review:
758199

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Abstract: This paper extends work of Fiedler, Jurkat and the present author to series of the form where is a moment sequence and . In the cases where it is possible to calculate it exactly, we find the best approximation to the sum of the series and the actual terms of the matrices involved. We have an advantage over accelerators commonly used for accelerating convergence in that we know explicitly the errors in our calculations.

**[1]**N. I. Achieser,*Theory of Approximation*(C. J. Hyman, Transl.), Ungar, New York, 1956. MR**0095369 (20:1872)****[2]**H. Fiedler & W. B. Jurkat, "On best approximations of alternating series,"*J. Approx. Theory*, v. 34, 1982, pp. 423-424. MR**656641 (83i:40001b)****[3]**W. B. Jurkat & B. L. R. Shawyer, "Best approximations of alternating series,"*J. Approx. Theory*, v. 34, 1982, pp. 397-422. MR**656640 (83i:40001a)****[4]**B. L. R. Shawyer, "Best approximation of alternating power series,"*J. Math. Anal. Appl.*(To appear.) MR**833592 (87g:41020)****[5]**D. A. Smith & W. F. Ford, "Acceleration of linear and logarithmic convergence,"*SIAM J. Numer. Anal.*, v. 16, 1979, pp. 223-240. MR**526486 (82a:65012)****[6]**D. A. Smith & W. F. Ford, "Numerical comparisons of nonlinear convergence accelerators,"*Math. Comp.*, v. 38, 1982, pp. 481-499. MR**645665 (83d:65014)**

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0758199-2

Article copyright:
© Copyright 1984
American Mathematical Society