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2011.43: A More Accurate Briggs Method for the Logarithm

2011.43: Awad H. Al-Mohy (2011) A More Accurate Briggs Method for the Logarithm.

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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 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2011.43
Deposited By:Awad Al-Mohy
Deposited On:28 May 2011

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