  We study a weighted low rank approximation that is inspired by a problem of
constrained low rank approximation of matrices as initiated by the work of
Golub, Hoffman, and Stewart (Linear Algebra and Its Applications, 88-89(1987),
317-327). Our results reduce to that of Golub, Hoffman, and Stewart in the
limiting cases. We also propose an algorithm based on the alternating direction
method to solve our weighted low rank approximation problem and compare it with
the state-of-art general algorithms such as the weighted total alternating
least squares and the EM algorithm.
