Algorithms for the Polar Decomposition

Abstract

For the polar decomposition of a square nonsingular matrix, Higham [SIAM J. Sci. Statist. Comput., 7 (1986), pp. 1160–1174] has given a reliable quadratically convergent algorithm that is based on Newton’s iteration. Motivated by Halley’s iteration, the author constructs a new family of methods that contains both methods (Higham's and Halley’s) as special cases. These methods generalize to rectangular matrices and some of them are also useful in computing the polar decomposition of rank deficient matrices.