COMPUTING HIGH SPEED CONVERGENT ITERATIVE METHODS FOR THE POLAR DECOMPOSITION.

This paper presents high speed convergent iterative methods for accelerating computation process in the polar decomposition of a matrix. As a first demonstration in our illustration, we split a complex number into real and imaginary components and simultaneously iterated to convergence using Halley’s third order iterative method for polynomial equation. Utilizing the Newton and Halley’s methods for computing polar decomposition of a matrix, we further accelerated convergence using matrix condition number and determinant of a matrix with a fast LU Factorization solver for matrix inversion. The described methods are backward stable.As a further insight of our study is the computation of zonal polynomials for these matrice., Numerical examples are demonstrated with these methods.