Asymptotic setting (revisited): analysis of a boundary-value problem and a relation to a classical approximation result

Abstract

Aiming at the asymptotic analysis of a class of nonlinear two-point boundary-value problems, we show a useful modification of the general result on the relation between the asymptotic and worst-case settings of information-based complexity (IBC). The modification is used to derive lower bounds on convergence rate of algorithms for solving a class of BVPs. Since matching upper bounds for this problem are known, the best convergence rate is established. The general result used in the asymptotic analysis of BVPs has potential applications beyond the typical IBC framework. We illustrate this by showing how the classical approximation result, (a version of) the Bernstein lethargy theorem, can be derived as a straightforward corollary from the general theorem.