A new family of multivariate matrix Padé approximants

• Jilali Abouir ^[1] ; Brahim Benouahmane ^[1] ; Abdelatif Elbouchouki ^[1]
  1. [1] Université Hassan II Mohammedia

     Université Hassan II Mohammedia

     Mohammedia, Marruecos

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 6, Nº. 2, 2014, págs. 199-217
• Idioma: inglés
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• Resumen

  • Padé-type approximants and Padé approximants are methods of rational approximation of a function which have a formal power series expansion. Padé and Pad´e-type approximants in the scalar case have been studied in many papers during a number of decades, (4, 6, 8, 9) to cite just a few. A generalization in the rectangular or homogeneous multivariate matrix case was given by Cheng De Zheng and Huaguang Zhang in (14, 15). In the present work we propose a more general definition of the Pad´e-type approximants and we will discuss their several algebraic properties which will be established. We introduce a new family of homogeneous multivariate matrix Padé approximants. Numerical examples are given to illustrate our results.