On matrix approximation problems with Ky Fank norms |
| |
Authors: | G. A. Watson |
| |
Affiliation: | (1) Department of Mathematics and Computer Science, University of Dundee, DD14HN Dundee, Scotland, UK |
| |
Abstract: | LetA be a realm xn matrix whose elements depend onl free parameters forming the vectorx. Then a class of approximation problems can be defined by the requirement thatx be chosen to minimize A(x), for a given matrix normon m ×n matrices. For example, it may be required to approximate a given matrix by a particular type of matrix, or by a linear combination of matrices. In the derivation of effective algorithms for such problems, a prerequisite is the provision of appropriate conditions satisfied by a solution, and the subdifferential of the matrix norm plays a crucial role in this. Therefore a characterization of the subdifferential is important, and this is considered for a class of orthogonally invariant norms known as Ky Fank norms, which include as special cases the spectral norm and the trace norm. The results lead to a consideration of efficient algorithms. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|