Key points are not available for this paper at this time.
The closest unitary matrix, measured in Euclidean norm, to a given rectangular matrix A is known to be the unitary factor in the polar decomposition of A. The paper gives a family of iterative methods of order of convergence p + 1, \, p = 1, 2, 3, , for computing this matrix. The methods are especially efficient when the columns of A are not too far from being orthonormal. The choice of order of convergence to minimize the amount of computation is discussed. Global convergence properties for the methods of order 4 are studied and sufficient conditions for convergence in terms of \| I - AH A \| are given.
Björck et al. (Tue,) studied this question.