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: | https://eprints.maths.manchester.ac.uk/id/eprint/1624 |
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