A quadratically convergent Newton method for computing the polar decomposition of a-rank matrix is presented and analysed. Acceleration parameters are introduced so as to enhance the rate of convergence and it is shown how reliable estimates of the optimal parameters may be computed practice. add to the known best approximation property of the unitary polar factor, the Hermitian polar H of a nonsingular Hermitian matrix A is shown to be a good positive definite approximation to A 1/2 (A / H) is shown to be a best Hermitian positive semi-definite approximation to A. Perturbation for the polar factors are derived. of the polar decomposition to factor analysis, aerospace computations and optimisation outlined; and a new method is derived for computing the square root of a symmetric positive definite.
Nicholas J. Higham (1986) studied this question.