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Mathematics of Computation

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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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0307438-2
Keywords: Logarithms, arctangents, iteration, Borchardt's algorithm, inverse circular functions, inverse hyperbolic functions, acceleration of convergence
Article copyright: © Copyright 1972 American Mathematical Society

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