B. Laszkiewicz, K. Ziêtak, 
Approximation of matrices and a family of Gander methods
 for polar decomposition, BIT Numer. Math. 46 (2006), 345-366.

Two matrix approximation problems are considered:
 approximation of a rectangular complex matrix
  by subunitary matrices with respect to unitarily invariant norms
   and a minimal rank approximation with respect to the spectral norm.

A characterization of a subunitary approximant 
of a square matrix with respect to the Schatten norms,
 given by Maher, is extended to the case of rectangular
  matrices and arbitrary unitarily invariant norms.

Iterative methods, based on the family of Gander methods
 and on Higham's scaled method for polar decomposition,
 are proposed for computing subunitary and minimal rank approximants. 
 Properties of Gander methods are  investigated in details.