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Series operations using minimum storage

Published online by Cambridge University Press:  17 February 2009

A. N. Stokes
A. N. Stokes
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, P.O. Box 310, South Melbourne, Victoria, 3025
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Abstract

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An algorithm is given for transforming a polynomial with n coefficients to a continued fraction accurate to the same order. Only n numbers are held in storage at each stage. An extension to produce an inverse polynomial, also accurate to order n, is described.

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 1 , April 1979 , pp. 84 - 89
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Henrici, P., “The quotient difference algorithm”, in Mathematical methods for digital computers (ed. Ralston, A. and Wilf, H. S.) (New York: Wiley, 1967), vol. 2.Google Scholar
[2]Henrici, P., Computational analysis with the HP-25 pocket calculator (New York: Wiley, 1977).Google Scholar
[3]Khovanskii, A. N., The application of continued fractions and their generalizations to problems in approximation theory (Groningen: Noordhoff, 1963).Google Scholar
[4]Knuth, D. E., The art of computer programming. Vol. 2. Seminumerical algorithms (Reading, Mass.: Addison-Wesley, 1969).Google Scholar
[5]Stokes, A. N., “A stable quotient-difference algorithm” (to appear).Google Scholar