On a new family of high-order iterative methods for the matrix pth root

  1. Amat, S. 1
  2. Ezquerro, J.A. 2
  3. Hernández-Verón, M.A. 2
  1. 1 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Numerical Linear Algebra with Applications

ISSN: 1070-5325

Any de publicació: 2015

Volum: 22

Número: 4

Pàgines: 585

Tipus: Article

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DOI: 10.1002/NLA.1974 SCOPUS: 2-s2.0-84935751733 WoS: WOS:000357833700001 GOOGLE SCHOLAR

Altres publicacions en: Numerical Linear Algebra with Applications

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Resum

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.