The so-called covering algorithm for enclosing the solution set of parameter—dependent systems of nonlinear equations has been recently proposed by Neumaier (The Enclosure of Solutions of Parameter Dependent Systems of Equations, in: Moore, R. E. (ed.), Reliability in Computing: The Role of Interval Methods in Scientific Computations, Academic Press, 1988). However, in the covering algorithm, only one box is processed in each iteration. This paper presents a parallelized version of the covering algorithm, in which all boxes present are processed simultaneously in each iteration. It is shown through several examples that this strategy results in speed-up of the algorithm by several orders of magnitude, particularly so in demanding problems. The proposed parallelized version can be run even on ordinary computers, i.e., it does not require a parallel computer.
Reliable Computing – Springer Journals
Published: Oct 21, 2004
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