Generation of $\alpha$-dense curves in infinite dimensional Banach spaces

Abstract

The so called $\alpha$-dense curves have an important role in the approximation of the solutions of certain problems involving functions of several variables, such as global optimization, numerical integration and many others. Roughly speaking, the $\alpha$-dense curves allow us, in certain sense, transform the given problem into a single variable one, thus eliminating the so called curse of dimensionality. In the present paper we show how construct $\alpha$-dense curves in infinite dimensional Banach spaces having a Schauder basis.