Error-Bounded Approximation of the Inverse of a Function Near an Extremum скачать в хорошем качестве

Error-Bounded Approximation of the Inverse of a Function Near an Extremum

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.