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

Zeitschrift:
Numerical Linear Algebra with Applications

ISSN: 1070-5325

Datum der Publikation: 2015

Ausgabe: 22

Nummer: 4

Seiten: 585

Art: Artikel

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

Andere Publikationen in: Numerical Linear Algebra with Applications

Projekte im Zusammenhang

Ecuaciones no lineales y métodos iterativos. Aplicaciones a problemas de optimización y ecuaciones matriciales. Nonlinear equations and iterative methods. Applications to optimization problems and matrix equations.

2015/00069/001

Procesos iteratios para resolver ecuaciones no lineales: construcción, convergencia, eficacia, análisis dinámico y aplicaciones

2012/00014/001

Zusammenfassung

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.