Inner Approximation of the Range of Vector-Valued Functions
نویسندگان
چکیده
No method for the computation of a reliable subset of the range of vector-valued functions is available today. A method for computing such inner approximations is proposed in the specific case where both domain and co-domain have the same dimension. A general sufficient condition for the inclusion of a box inside the image of a box by a continuously differentiable vector-valued is first provided. This sufficient condition is specialized to a more efficient one, which is used in a specific bisection algorithm that computes reliable inner and outer approximations of the image of a domain defined by constraints. Some experimentations are presented. (Reliable Computing volume 14, pp. 1–23, June, 2010) Submitted: December 7, 2005; Accepted: January 10, 2008.
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عنوان ژورنال:
- Reliable Computing
دوره 14 شماره
صفحات -
تاریخ انتشار 2010