Randomized Kolmogorov and Linear Widths on Generalized Besov Classes with Mixed Smoothness

Abstract

In this paper, we study the Kolmogorov and the linear widths on the generalized Besov sov classes , BpθΩ with mixed smoothness in the Monte Carlo setting. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of the Kolmogorov and the linear widths for some values of the parameters p,q,θ.