You are here: MIMS > EPrints
MIMS EPrints

2006.185: Newton's method for the matrix square root

2006.185: Nicholas J. Higham (1986) Newton's method for the matrix square root. Mathematics of Computation, 46 (174). pp. 537-549. ISSN 00255718

Full text available as:

PDF - Archive staff only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
1012 Kb

Official URL: http://www.jstor.org/browse/00255718/di970598?frame=noframe&userID=82587baa@man.ac.uk/01cc99333c00501e40617&dpi=3&config=jstor

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 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2006.185
Deposited By:Miss Louise Stait
Deposited On:06 July 2006

Download Statistics: last 4 weeks
Repository Staff Only: edit this item