A More Accurate Briggs Method for the Logarithm

Al-Mohy, Awad H. (2011) A More Accurate Briggs Method for the Logarithm. [MIMS Preprint]

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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.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Awad Al-Mohy
Date Deposited: 28 May 2011
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1624

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