Our report presents a survey of modern interval existence tests for the solutions of nonlinear systems of equations in finite-dimensional spaces. For a number of tests based on Brouwer fixed-point theorem, we develop modifications that rely, first, on the idea of bicentric interval extension of functions and, second, on the restriction of the tested domain to the boundary of the box under consideration only. When applied both separately and in combination with each other, our improvements allow one to substatially increase computational efficiency of the procedures for the global verified solution of nonlinear systems of equations using adaptive branch-and- prune search.
Note. Abstracts are published in author's edition
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