The next meeting of the seminar of the

Mathematical Modeling and Numerical Analysis Department

will be held on June 15, 2017 (Thursday) at 14:00 in room 403 of the Institute of Mathematics and Informatics.

A talk on

On best uniform approximation by low-rank matrices

will be delivered by Clemens Hofreither, Institute of Computational Mathematics, Johannes Kepler University, Linz, Austria.

Abstract. We study the problem of best approximation, in the elementwise maximum norm,of a given matrix by another matrix of lower rank.

We generalize a recent result by Pinkus that describes the bestapproximation error in a class of low-rank approximation problems and givean elementary proof for it.Based on this result, we describe the best approximation error and theerror matrix in the case of approximation by a matrix of rank one lessthan the original one.

For the case of approximation by matrices with arbitrary rank, we givelower and upper bounds for the best approximation error in terms ofcertain submatrices of maximal volume.

We illustrate our results using $2 times 2$ matrices as examples,for which we also give a simple closed form of the bestapproximation error.