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Evaluation of Complex Logarithms and Related Functions

George J. Miel
SIAM Journal on Numerical Analysis
Vol. 18, No. 4 (Aug., 1981), pp. 744-750
Stable URL: http://www.jstor.org/stable/2157293
Page Count: 7
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Evaluation of Complex Logarithms and Related Functions
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Abstract

An algorithm is presented for computing ln z with complex arithmetic, by extending to the complex plane Carlson's treatment of a classical iteration using arithmetic and geometric means. Although not competitive with current techniques which handle the real and imaginary parts separately, the algorithm may be useful in special purpose applications. A detailed analysis of convergence, scaling, and roundoff is given. Standard identities and some minor bookkeeping allow the evaluation of inverse circular and inverse hyperbolic functions. It is also shown that the basic procedure is related to certain real algorithms.

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