Recursive low-rank trunction of matrices

Vortrag von Prof. Dr. Wolfgang Hackbusch

Sprecher eingeladen von: Prof. Dr. Stefan Sauter

Datum: 08.12.22  Zeit: 17.00 - 18.30  Raum: 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.