# Best m-term approximation of the "step-function" and related problems

ASCW01 - Challenges in optimal recovery and hyperbolic cross approximation

The main point of the talk is  the problem of approximation    of the step-function by $m$-term trigonometric polynomials  and some closely related problems: the approximate rank of a specific triangular matrix,  the Kolmogorov width of BV functions. This problem has its origins  in approximation theory (best sparse approximation and Kolmogorov widths) as well as in computer science (approximate rank of a matrix). There are different approaches and techniques: $\gamma_2$—norm, random approximations, orthomassivity of a set….  I plan to show what can be achieved by these techniques.

This talk is part of the Isaac Newton Institute Seminar Series series.