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A parallel root-finding algorithm
Published online by Cambridge University Press: 01 December 2015
Abstract
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We present a parallel algorithm to calculate a numerical approximation of a single, isolated root 
${\it\alpha}$ of a function 
$f:\mathbb{R}\rightarrow \mathbb{R}$ which is sufficiently regular at and around 
${\it\alpha}$. The algorithm is derivative free and performs one function evaluation on each processor per iteration. It requires at least three processors and can be scaled up to any number of these. The order with which the generated sequence of approximants converges to 
${\it\alpha}$ is equal to 
$(n+\sqrt{n^{2}+4})/2$ for 
$n+1$ processors with 
$n\geqslant 2$. This assumes that particular combinations of the derivatives of 
$f$ do not vanish at 
${\it\alpha}$.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © The Author 2015
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