Journal Article10.1007/BF02252197
Algorithm 38 two computer codes for convergence acceleration
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TL;DR: Two computer codes for calculating the sum of power series belonging to a certain general class are described and the use of the codes for an illustrative test example is explained.
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Abstract: This paper describes two computer codes for calculating the sum of power series, belonging to a certain general class. The use of the codes for an illustrative test example is explained.
read more
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Citations
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The practical use of the Euler transformation
TL;DR: The generalised Euler transformation as mentioned in this paper is a powerful transformation of infinite series which can be used, in theory, for the acceleration of convergence and for analytic continuation, but when applied to a series with rounded coefficients, its behaviour can differ substantially from that predicted theoretically.
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A note on the summation of power series
TL;DR: In this article, a compact and convenient formula for the evaluation of the approximants in terms of the sequence of partiak sums of the series is presented and this is compared with the corresponding measure for the generalized Euler transformation and for the original sequence of partial sums.
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References
Convergence acceleration on a general class of power series
TL;DR: Several efficient methods for evaluating functions defined by power series expansions by investigating theoretically and physically the convergence rates of the proposed computational schemes.
33
Numerical computation of an integral appearing in the Fröman-Fröman phase-integral formula for calculation of quantal matrix elements without the use of wave functions
TL;DR: In this paper, an efficient method for the numerical treatment of an integral appearing in the Froman-Froman phaseintegral formula is presented, and the stability and convergence of the method are verified for a large class of integrands.
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