Error-Bounded Approximation of the Inverse of a Function Near an Extremum
Автор: Interval methods in control engineering
Загружено: 2024-12-06
Просмотров: 71
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Speaker:
Christophe Jermann (Université de Nantes, France)
Abstract:
Computing the inverse of a function is an important operation in interval-based solving: It makes it possible to reduce the domains of the variables of a problem, "projecting" known bounds on the functions. Approximating the inverse is a good way to counter the shortcomings of interval arithmetic and to reduce the computation time. Computing such an approximation is difficult in the vicinity of the optima of a function: its inverse has an infinite derivative there.
In this talk, we present a way of deriving a polynomial approximation of a monotonic function on a domain where it has an extremum, with a guaranteed error bound. The approach will be illustrated on the inverse approximation of the binary Gibbs entropy function used in thermodynamics, with a sufficient error bound for the needs of interval optimization algorithms.
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