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
Año de publicación: 2015
Volumen: 22
Número: 4
Páginas: 585
Tipo: Artículo
beta Ver similares en nube de resultadosOtras publicaciones en: Numerical Linear Algebra with Applications
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Resumen
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.