Parallelization Method for a Continuous Property |
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Authors: | Paweł Pilarczyk |
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Institution: | 1. Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal
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Abstract: | An automated general purpose method is introduced for computing a rigorous estimate of a bounded region in ℝ
n
whose points satisfy a given property. The method is based on calculations conducted in interval arithmetic and the constructed
approximation is built of rectangular boxes of variable sizes. An efficient strategy is proposed, which makes use of parallel
computations on multiple machines and refines the estimate gradually. It is proved that under certain assumptions the result
of computations converges to the exact result as the precision of calculations increases. The time complexity of the algorithm
is analyzed, and the effectiveness of this approach is illustrated by constructing a lower bound on the set of parameters
for which an overcompensatory nonlinear Leslie population model exhibits more than one attractor, which is of interest from
the biological point of view. This paper is accompanied by efficient and flexible software written in C++ whose source code
is freely available at . |
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Keywords: | |
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