On a new family of high-order iterative methods for the matrix pth root
- Amat, S. 1
- Ezquerro, J.A. 2
- Hernández-Verón, M.A. 2
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1
Universidad Politécnica de Cartagena
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2
Universidad de La Rioja
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ISSN: 1070-5325
Year of publication: 2015
Volume: 22
Issue: 4
Pages: 585
Type: Article
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Abstract
The main goal of this paper is to approximate the principal pth root of a matrix by using a family of high-order iterative methods. We analyse the semi-local convergence and the speed of convergence of these methods. Concerning stability, it is well known that even the simplified Newton method is unstable. Despite it, we present stable versions of our family of algorithms. We test numerically the methods: we check the numerical robustness and stability by considering matrices that are close to be singular and badly conditioned. We find algorithms of the family with better numerical behavior than the Newton and the Halley methods. These two algorithms are basically the iterative methods proposed in the literature to solve this problem. © 2015John Wiley & Sons, Ltd.