On a generalized matrix approximation problem in the spectral norm
Kin Cheong Sou, Anders Rantzer
In this paper theoretical results regarding a generalized minimum rank matrix approximation problem in the spectral norm are presented. An alternative solution expression for the generalized matrix approximation problem is obtained. This alternative expression provides a simple characterization of the achievableminimum rank, which is shown to be the same as the optimal objective value of the classical problem considered by Eckart–Young–Schmidt–Mirsky, as long as the generalized problem is feasible. In addition, this paper provides a result on a constrained version of the matrix approximation problem, establishing that the later problem is solvable via singular value decomposition.
matrix approximation, rank minimization, singular value decomposition
Linear Algebra and its Applications, 436:7, pp. 2331–2341, November 2012.