Newton's Method for the Matrix Square Root
Nicholas John Higham · Mathematics of Computation · 1986
One approach to computing a square root of a matrix A is to apply Newton's method to the quadratic matrix equation F(X) ≡X2 - A = 0. Two widely-quoted matrix square root iterations obtained by rewriting this Newton iteration are shown to have excellent mathematical convergence properties. However, by means of a perturbation analysis and supportive numerical examples, it is shown that these simplified iterations are numerically unstable. A further variant of Newton's method for the matrix square root, recently proposed in the literature, is shown to be, for practical purposes, numerically stable.