Talk
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.