## 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

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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 |
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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 |

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