The next meeting of the seminar of the

Mathematical Modeling and Numerical Analysis Department

will be held on May 26, 2016 (Monday) at 14:00 in room 403 of the Institute of Mathematics and Informatics.

A talk on

On best uniform approximation with low-rank matrices

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

Abstract. Given a matrix, we study the best-approximation error by a matrix of lower rank. Here we are interested in a class of elementwise norms, of which the Frobenius and the Chebyshev (entrywise maximum) norms are special cases. Based on a result by A. Pinkus (2012), we derive both lower and upper bounds for the best-approximation error by a rank k matrix in the maximum norm. The quantities used in the estimates are absolute determinants of certain maximal submatrices, and we establish some connections to the theory of pseudoskeleton approximation, where this "maximal volume concept" has been applied previously. We illustrate the results by the simple example of some 2x2 matrices.