A parallelized version of the covering algorithm for solving parameter-dependent systems of nonlinear equations

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.