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Abstract This paper deals with the empirical convergence speed of inclusion functions applied in interval methods for global optimization. According to our experience the natural interval extension of a given function can be as good as a usual quadratically convergent inclusion function, and although centered forms are in general only of second-order, they can perform as one of larger convergence order. These facts indicate that the theoretical convergence order should not be the only indicator of the quality of an inclusion function, it would be better to know which inclusion function can be used most efficiently in concrete instances. For this reason we have investigated the empirical convergence speed of the usual inclusion functions on some test functions. [ABSTRACT FROM AUTHOR]

Abstract: In a previous paper, the author introduced a new class of multivariate rational interpolants, which are called Optimal Padé-type Approximants (OPTA). There, for this class of rational interpolants, which extends classical univariate Padé Approximants, a direct extension of the “de Montessus de Ballore''s Theorem” for meromorphic functions in several variables is established. In the univariate case, this theorem ensures uniform convergence of a row of Pade Approximants when the denominator degree equals the number of poles (counting multiplicities) in a certain disc. When one overshoots the number of poles when fixing the denominator degree, convergence in measure or capacity has been proved and, under certain additional restrictions, the uniform convergence of a subsequence of the row. The author tackles the latter case and studies its generalization to functions in several variables by using OPTA. [Copyright &y& Elsevier]