An algorithm for computing logarithms and arctangents
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- by B. C. Carlson PDF
- Math. Comp. 26 (1972), 543-549 Request permission
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.References
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- B. C. Carlson, The logarithmic mean, Amer. Math. Monthly 79 (1972), 615–618. MR 302842, DOI 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 10.1090/S0025-5718-1961-0135228-5
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 543-549
- MSC: Primary 65D20
- DOI: https://doi.org/10.1090/S0025-5718-1972-0307438-2
- MathSciNet review: 0307438