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2006.395: Algorithms for the Matrix p'th Root

2006.395: Dario A. Bini, Nicholas J. Higham and Beatrice Meini (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
Additional Information:

Uncontrolled Keywords:matrix pth root, matrix sign function, Wiener–Hopf factorization, Newton’s method, Graeffe iteration, cyclic reduction, Laurent polynomial
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2006.395
Deposited By:Nick Higham
Deposited On:27 October 2006

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