Name
Abstract | ||
|---|---|---|
We relate the problem of best low-rank approximation in the spectral norm for a matrix A to Kolmogorov n-widths and corresponding optimal spaces. We characterize all the optimal spaces for the image of the Euclidean unit ball under A, and we show that any orthonormal basis in an n-dimensional optimal space generates a best rank-n approximation to A. We also present a simple and explicit construction to obtain a sequence of optimal n-dimensional spaces once an initial optimal space is known. This results in a variety of solutions to the best low-rank approximation problem and provides alternatives to the truncated singular value decomposition. This variety can be exploited to obtain best low-rank approximations with problem-oriented properties. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1137/20M1355720 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | DocType | Volume |
low-rank approximation, best approximation, n-widths, optimal spaces | Journal | 42 |
Issue | ISSN | Citations |
1 | 0895-4798 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael S. Floater | 1 | 1333 | 117.22 |
| Carla Manni | 2 | 385 | 35.70 |
| Espen Sande | 3 | 0 | 0.34 |
| Hendrik Speleers | 4 | 236 | 24.49 |