Newton's method for the matrix square root

Author:
Nicholas J. Higham

Journal:
Math. Comp. **46** (1986), 537-549

MSC:
Primary 65F30; Secondary 65H10

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829624-5

MathSciNet review:
829624

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Abstract | References | Similar Articles | Additional Information

Abstract: One approach to computing a square root of a matrix *A* is to apply Newton's method to the quadratic matrix equation . 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829624-5

Keywords:
Matrix square root,
Newton's method,
numerical stability

Article copyright:
© Copyright 1986
American Mathematical Society