On greedy algorithm approximating Kolmogorov widths in Banach spaces - Wojtaszczyk, P. (Journal of mathematical analysis and applications, 2015)
The greedy algorithm to produce n-dimensional subspaces Xn to approximate a compact set F contained in a Hilbert space was introduced in the context of reduced basis method in [12,13]. The same algorithm works for a general Banach space and in this context was studied in [4]. In this paper we study the case F⊂Lp. If Kolmogorov diameters dn(F) of F decay as n−α we give an almost optimal estimate for the decay of σn:=dist(F,Xn). We also give some direct estimates of the form σn≤Cndn(F).