Norms of random submatrices and sparse approximation

Abstract: Many problems in the theory of sparse approximation require bounds on operator norms of a random submatrix drawn from a fixed matrix. The purpose of this Note is to collect estimates for several different norms that are most important in the analysis of minimization algorithms. Several of these bounds have not appeared in detail. To cite this article: J.A. Tropp, C. R. Acad. Sci. Paris, Ser. I 346 (2008). [Copyright &y& Elsevier]