Variable projection for affinely structured low-rank approximation in   weighted 2-norms
  The structured low-rank approximation problem for general affine structures, weighted 2-norms and fixed elements is considered. The variable projection principle is used to reduce the dimensionality of the optimization problem. Algorithms for evaluation of the cost function, the gradient and an approximation of the Hessian are developed. For $m \times n$ mosaic Hankel matrices the algorithms have complexity $O(m^2 n)$. 
Konstantin Usevich and Ivan Markovsky
math.OC math.NA