On the approximate minimization of functionals

摘要: This paper considers in general the problem of finding minimum a given functional f(u) over set B by approximately minimizing sequence functionals fn(un) "discretized" Bn; theorems are proving convergence approximating points un Bn to desired point u B. Applications Rayleigh-Ritz method, regularization, Chebyshev solution differential equations, and calculus variations. 1. Introduction. Many theoretical computational problems either arise or can be formulated as one locating some real-valued (non- linear) certain set; such variational settings often lead existence well methods for solving question. Computationally, however, is generally forced deal with discrete data place original functional; it therefore necessary analyze relationships between their discretized analogues. In (7, Section 4), we first studied under equicontinuity assumptions question nearby functionals. this present note state generally, give theorems, describe particular examples.