Abstract
A method is investigated by which tight bounds on the range of a multivariate rational function over a box can be computed. The approach relies on the expansion of the numerator and denominator polynomials in Bernstein polynomials. Convergence of the bounds to the range with respect to degree elevation of the Bernstein expansion, to the width of the box and to subdivision are proven and the inclusion isotonicity of the related enclosure function is shown.
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CITATION STYLE
Garloff, J., & Hamadneh, T. (2016). Convergence and inclusion isotonicity of the tensorial rational bernstein form. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9553, pp. 171–179). Springer Verlag. https://doi.org/10.1007/978-3-319-31769-4_14
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