Journal Title
Title of Journal: MathComputSci
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Abbravation: Mathematics in Computer Science
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Authors: Elke Just
Publish Date: 2014/08/09
Volume: 8, Issue: 3-4, Pages: 341-355
Abstract
Most verified solvers for nonlinear interval systems of equations comprise two strategies a branchandboundtype “location” phase for excluding regions that cannot contain a solution and a “verification” phase for proving that the remaining regions do indeed contain solutions In the first phase subdivision is crucial for the efficiency of the solvers We discuss several ways for subdivision and present robust strategies that are suited for a variety of nonlinear systems Particular focus is on the choice of subdivision directions subdivision points and the handling of unbounded intervals Furthermore we discuss a method to discard parts of a box within subdivision Numerical evaluations are given based on the nonlinear interval solver SONIC In the verification phase further subdivision can increase the strength of the verification tests In this paper we address methods for the rigorous implementation of symmetrical subdivision which is needed eg in existence tests based on Borsuk’s theorem
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