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

Presented by: 
Konstantin Ryutin
Date: 
Thursday 21st February 2019 - 09:40 to 10:15
Venue: 
INI Seminar Room 1
Abstract: 
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons