Interval Bounds for Stationary Values of Functionals.

摘要

A number of important problems in applied mathematics can be reduced to finding stationary values of functionals (maxima, minima, and critical values). For functionals defined in terms of integrals, the method of interval integration provides a way to obtain interval (two-sided) bounds for these stationary values. As a special case of this method, upper and lower bounds for eigenvalues of linear operators can be obtained. The inclusion of stationary values in intervals is based on the use of interval functions which include the function for which the functional is stationary, and its derivatives. A simple way to construct such interval functions is given, and examples are presented of a minimum and an eigenvalue problem. The improvement of initial results by iteration is indicated. (Author)