This paper presents a novel set-based computing method, called intervalsuperposition arithmetic, for enclosing the image set of multivariatefactorable functions on a given domain. In order to construct such enclosures,the proposed arithmetic operates over interval superposition models which areparameterized by a matrix with interval components. Every point in the domainof a factorable function is then associated with a sequence of components ofthis matrix and the superposition, i.e. Minkowski sum, of these elementsencloses the image of the function at this point. Interval superpositionarithmetic has a linear runtime complexity with respect to the number ofvariables. Besides presenting a detailed theoretical analysis of the accuracyand convergence properties of interval superposition arithmetic, the paperillustrates its advantages compared to existing set arithmetics via numericalexamples.

Interval Superposition Arithmetic

Mario E. Villanueva;
2016

Abstract

This paper presents a novel set-based computing method, called intervalsuperposition arithmetic, for enclosing the image set of multivariatefactorable functions on a given domain. In order to construct such enclosures,the proposed arithmetic operates over interval superposition models which areparameterized by a matrix with interval components. Every point in the domainof a factorable function is then associated with a sequence of components ofthis matrix and the superposition, i.e. Minkowski sum, of these elementsencloses the image of the function at this point. Interval superpositionarithmetic has a linear runtime complexity with respect to the number ofvariables. Besides presenting a detailed theoretical analysis of the accuracyand convergence properties of interval superposition arithmetic, the paperillustrates its advantages compared to existing set arithmetics via numericalexamples.
Mathematics, Numerical Analysis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/21638
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