# Algorithms for the Matrix p'th Root

Bini, Dario A. and Higham, Nicholas J. and Meini, Beatrice (2005) Algorithms for the Matrix p'th Root. Numerical Algorithms, 39 (4). pp. 349-378. ISSN 1572-9265

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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.

Item Type: Article matrix pth root, matrix sign function, Wiener–Hopf factorization, Newton’s method, Graeffe iteration, cyclic reduction, Laurent polynomial MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theoryMSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis Nick Higham 27 Oct 2006 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/635

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