Presentation of a highly tuned multithreaded interval solver for underdetermined and well-determined nonlinear systems

Abstract

The paper summarizes author's investigations in tuning a multithreaded interval branch-and-prune algorithm for nonlinear systems and presents the developed solver. New results for using the box-consistency enforcing operator and a new variant of the initial exclusion phase are presented. Also, a new heuristic to choose the coordinate for bisection is considered. Extensive numerical experiments are analyzed to provide the satisfying version of the algorithm.

Developing an interval method for training denoising autoencoders by bounding the noise

“…The 'rejection/reduction tests', mentioned in the algorithm have been described in the author's previous papers; specifically, please consult [25], [26], [27], [28] and the references therein.…”

“…In a series of earlier papers, including [25], [26], [27], [28], the author has introduced his solver HIBA_USNE (Heuristical Interval Branch-and-prune Algorithm for Underdetermined and well-determined Systems of Nonlinear Equations) [29]. It was also used in [4] to analyze a Hopfield-like neural network.…”