An algorithm for computing logarithms and arctangents
Author:
B. C. Carlson
Journal:
Math. Comp. 26 (1972), 543-549
MSC:
Primary 65D20
DOI:
https://doi.org/10.1090/S0025-5718-1972-0307438-2
MathSciNet review:
0307438
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Abstract | References | Similar Articles | Additional Information
Abstract: An iterative algorithm with fast convergence can be used to compute logarithms, inverse circular functions, or inverse hyperbolic functions according to the choice of initial conditions. Only rational operations and square roots are required. The method consists in adding an auxiliary recurrence relation to Borchardt’s algorithm to speed the convergence.
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- B. C. Carlson, Algorithms involving arithmetic and geometric means, Amer. Math. Monthly 78 (1971), 496–505. MR 283246, DOI https://doi.org/10.2307/2317754
- B. C. Carlson, The logarithmic mean, Amer. Math. Monthly 79 (1972), 615–618. MR 302842, DOI https://doi.org/10.2307/2317088 J. F. Hart et al., Computer Approximations, Wiley, New York, 1968.
- Eduard L. Stiefel, An introduction to numerical mathematics, Academic Press, New York-London, 1963. Translated by Werner C. Rheinboldt and Cornelie J. Rheinboldt. MR 0181077
- Henry C. Thacher Jr., Iterated square root expansions for the inverse cosine and inverse hyperbolic cosine, Math. Comp. 15 (1961), 399–403. MR 135228, DOI https://doi.org/10.1090/S0025-5718-1961-0135228-5
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Additional Information
Keywords:
Logarithms,
arctangents,
iteration,
Borchardt’s algorithm,
inverse circular functions,
inverse hyperbolic functions,
acceleration of convergence
Article copyright:
© Copyright 1972
American Mathematical Society
