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Riccati acceleration of Jacobi continued fractions and Laguerre-Hahn orthogonal polynomials

Part of the Lecture Notes in Mathematics book series (LNM,volume 1071)

Abstract

The evaluation of slowly convergent continued fractions α1/(β12/(β2+...)) can be made more efficient by replacing an approximant α1/(β12/(β2+...+αrr)) by a modified approximant α1/(β12/(β2+...+αr/(βrr))), according to work done by Thron, Waadeland and Jacobsen. The convergence factor should of course be a reasonably good approximation to the tail αr+1/(βr+1+...).

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Magnus, A. (1984). Riccati acceleration of Jacobi continued fractions and Laguerre-Hahn orthogonal polynomials. In: Werner, H., Bünger, H.J. (eds) Padé Approximation and its Applications Bad Honnef 1983. Lecture Notes in Mathematics, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099620

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  • DOI: https://doi.org/10.1007/BFb0099620

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