, Volume 39, Issue 4, pp 349-378

Algorithms for the matrix pth root

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Abstract

New theoretical results are presented about the principal matrix pth root. In particular, we show that the pth root is related to the matrix sign function and to the Wiener–Hopf factorization, and that it can be expressed as an integral over the unit circle. These results are used in the design and analysis of several new algorithms for the numerical computation of the pth root. We also analyze the convergence and numerical stability properties of Newton’s method for the inverse pth root. Preliminary computational experiments are presented to compare the methods.

Communicated by C. Brezinski

AMS subject classification

15A24, 65H10, 65F30
Numerical Analysis Report 454, Manchester Centre for Computational Mathematics, July 2004.
Dario A. Bini: This work was supported by MIUR, grant number 2002014121.
Nicholas J. Higham: This work was supported by Engineering and Physical Sciences Research Council grant GR/R22612 and by a Royal Society – Wolfson Research Merit Award.