# Low rank approximation of matrix under $l_2$ norm

Theorem 14 of this paper by Tam´as Sarl´os gives a relative error rank-$k$ approximation of a given matrix $A$ under the frobenius norm. I am looking for reference of a similar result (relative error low rank approximation) under the $l_2$ norm.

Pls let me know I am able to put the question clearly.

• "$l_2$ norm" ​ = ​ "Euclidean operator norm" ​ ​ ​ ? ​ ​ ​ ​ ​ ​ ​ ​ – user6973 Jan 11 '16 at 9:37
• @RickyDemer Yes. – Ram Jan 11 '16 at 9:42

## 1 Answer

This is the median k-flat problem. Feldman wrote some papers on this and related problems. See for example http://arxiv.org/abs/1106.1379 .