Modul: MAT870 Zurich Colloquium in Applied and Computational Mathematics

## Recursive low-rank trunction of matrices

Talk by Prof. Dr. Wolfgang Hackbusch

Speaker invited by: Prof. Dr. Stefan Sauter

**Date:** 08.12.22 **Time:** 17.00 - 18.30 **Room:** Y27H28

The best approximation of a matrix by a low-rank matrix can be obtained by the singular value decomposition. For large-sized matrices this approach is too costly. Instead we use a block decomposition. Approximating the small submatrices by low-rank matrices and agglomerating them into a new, coarser block decomposition, we obtain a recursive method. The required computational work is O(rnm) where r is the desired rank and nxm is the size of the matrix. We discuss error estimates for A-B and M-A where A is the result of the recursive trunction applied to M, while B is the best rank-r approximation. Numerical tests show that the approximate trunction is very close to the best one.