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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Best approximation of positive power series

Author: B. L. R. Shawyer
Journal: Math. Comp. 43 (1984), 529-534
MSC: Primary 41A10; Secondary 41A50
MathSciNet review: 758199
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Abstract: This paper extends work of Fiedler, Jurkat and the present author to series of the form $\Sigma {a_n}{x^n}$ where $\{ {a_n}\}$ is a moment sequence and $0 < x < 1$. In the cases where it is possible to calculate it exactly, we find the best ${L^p}$ 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.

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Article copyright: © Copyright 1984 American Mathematical Society