Newton's method for the matrix square root

Higham, Nicholas J. (1986) Newton's method for the matrix square root. Mathematics of Computation, 46 (174). pp. 537-549. ISSN 00255718

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Abstract

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.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Ms Lucy van Russelt
Date Deposited: 06 Jul 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/368

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