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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Constrained intervals and interval spaces

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Author(s):
Lodwick, Weldon A. [1, 2] ; Jenkins, Oscar A. [1]
Total Authors: 2
Affiliation:
[1] Univ Colorado, Dept Math, Denver, CO 80204 - USA
[2] UNESP, Dept Matemat Aplicada, Sao Jose Do Rio Preto - Brazil
Total Affiliations: 2
Document type: Journal article
Source: SOFT COMPUTING; v. 17, n. 8, SI, p. 1393-1402, AUG 2013.
Web of Science Citations: 10
Abstract

Constrained intervals, intervals as a mapping from {[}0, 1] to polynomials of degree one (linear functions) with non-negative slopes, and arithmetic on constrained intervals generate a space that turns out to be a cancellative abelian monoid albeit with a richer set of properties than the usual (standard) space of interval arithmetic. This means that not only do we have the classical embedding as developed by H. Radstrom, S. Markov, and the extension of E. Kaucher but the properties of these polynomials. We study the geometry of the embedding of intervals into a quasilinear space and some of the properties of the mapping of constrained intervals into a space of polynomials. It is assumed that the reader is familiar with the basic notions of interval arithmetic and interval analysis. (AU)

FAPESP's process: 11/13985-0 - Generalized uncertainty applied to optimization
Grantee:Geraldo Nunes Silva
Support type: Research Grants - Visiting Researcher Grant - International