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Efficient algorithm for minimal-rank matrix approximations (1994).
| Content Provider | CiteSeerX |
|---|---|
| Author | Veen, Alle-Jan Van Der |
| Abstract | For a given matrix H which has d singular values larger than e, an expression for all rank-d approximants H such that (H- H) has 2-norm less than e is derived. These approximants have minimal rank, and the set includes the usual `truncated SVD' low-rank approximation. The main step in the procedure is a generalized Schur algorithm, which requires only O(1/2 m 2 n) operations (for an m n matrix H). The column span of the approximant is computed in this step, and updating and downdating of this space is straightforward. The algorithm is amenable to parallel implementation. 1 Introduction Let H be a given m n matrix, having d singular values larger than 1 and none equal to 1. Denote by k k the matrix 2-norm. In this paper, we describe an algorithm to compute all possible matrices H such that (a) k H - H k 1 , (b) rank( H) = d . Such a matrix H is a low-rank approximation of H in 2-norm. The problem can be generalized trivially by scaling H, in which case we compute H ... |
| File Format | |
| Publisher Date | 1994-01-01 |
| Access Restriction | Open |
| Subject Keyword | Minimal-rank Matrix Approximation Efficient Algorithm Singular Value Low-rank Approximation Generalized Schur Algorithm Column Span Rank-d Approximants Introduction Let Possible Matrix Minimal Rank Main Step |
| Content Type | Text |
