Rotation Matrix and Angles of Rotation in the Polar Decomposition

Abstract

This paper aims at computing the rotation matrix and angles of rotations using Newton and Halley’s methods in the generalized polar decomposition. The method extends the techniques of Newton’s and Halley’s methods for iteratively finding the zeros of polynomial equation of single variable to matrix rotation valued problems. It calculates and estimates the eigenvalues using Chevbyshev’s iterative method while computing the rotation matrix. The sample problems were tested on a randomly generated matrix of order from the family of matrix market. Numerical examples are given to demonstrate the validity of this work.