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MiS Preprint

New Estimates for the Recursive Low-Rank Truncation

Wolfgang Hackbusch


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 one may use a block decomposition. Approximating the small submatrices by low-rank matrices and agglomerating them into a new, coarser block decomposition, one obtains a recursive method. The required computation work is $O(rnm)$ if $r$ is the desired rank and $n\times m$ is the size of the matrix. The paper discusses the error $A-B$, where $A$ is the result of the recursive truncation, while $B$ is the best approximation.

MSC Codes:
65Fxx, 65F30, 15A18, 15A45
low-rank approximation, singular value decomposition, error estimate, Hierarchical matrix

Related publications

2016 Repository Open Access
Wolfgang Hackbusch

New estimates for the recursive low-rank truncation of block-structured matrices

In: Numerische Mathematik, 132 (2016) 2, pp. 303-328