Abstract
A new approach for computing an expression of the form \(a^{1/2^k}-1\) is presented that avoids the danger of subtractive cancellation in floating point arithmetic, where a is a complex number not belonging to the closed negative real axis and k is a nonnegative integer. We also derive a condition number for the problem. The algorithm therefore allows highly accurate numerical calculation of log(a) using Briggs’ method.
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Version of August 5, 2011.
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Al-Mohy, A.H. A more accurate Briggs method for the logarithm. Numer Algor 59, 393–402 (2012). https://doi.org/10.1007/s11075-011-9496-z
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DOI: https://doi.org/10.1007/s11075-011-9496-z