On the stability of a class of convergence acceleration methods for power series |
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Authors: | Sven-Åke Gustafson |
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Institution: | (1) Centre for Mathematical Analysis, Australian National University, G.P.O. Box 4, 2601 Canberra City, ACT, Australia;(2) Department of Numerical Analysis, Royal Institute of Technology, S-10044 Stockholm 70, Sweden |
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Abstract: | In this paper we study the problem of evaluating the sum of a power series whose terms are given numerically with a moderate accuracy. For a large class of divergent series a sum may be defined using analytic continuation. This sum may be estimated using the values of a finite number of terms. However, it is established here that the accuracy of this estimate will generally deteriorate if we use an ever-growing number of terms. A result on the stability of product quadrature is also obtained as a corollary of our main stability theorem.Dedicated to professor Germund Dahlquist, on the occasion of his 60th birthday |
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Keywords: | 65B10 65G99 |
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