2010•Unpublished venueRequires access

Solution Sets of Complex Linear Interval Systems of Equations.

Milan Hladík

Open publisher page 18 citations

Abstract

We present a solution set description for systems of complex interval equations, where complex intervals have a rectangular form. The solution set is described by a system of nonlinear inequalities, which can be used to obtain a very accurate approximation of the interval hull of the solution set. In our numerical experiments we exploit this approximation to study overestimation for common complex interval equation solvers (Gauss elimination, Hansen-Bliek-Rohn-Ning-Kearfott method).

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What this paper is about

We present a solution set description for systems of complex interval equations, where complex intervals have a rectangular form. The solution set is described by a system of nonlinear inequalities, which can be used to obtain a very accurate approximation of the interval hull of the solution set. In our numerical experiments we exploit this approximation to study overestimation for common complex interval equation solvers (Gauss elimination, Hansen-Bliek-Rohn-Ning-Kearfott method).

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Available abstract

We present a solution set description for systems of complex interval equations, where complex intervals have a rectangular form. The solution set is described by a system of nonlinear inequalities, which can be used to obtain a very accurate approximation of the interval hull of the solution set. In our numerical experiments we exploit this approximation to study overestimation for common complex interval equation solvers (Gauss elimination, Hansen-Bliek-Rohn-Ning-Kearfott method).

Key concepts: Interval (graph theory), Mathematics, Interval arithmetic, Solution set, Set (abstract data type), Nonlinear system, Linear system, Applied mathematics

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