Un algoritmo cuasi-Newton para resolver la ecuación cuadrática matricial

• Macías, Mauricio ^[1] ; Martínez, Héctor J. ^[2] ; Pérez, Rosana ^[1]
  1. [1] Universidad del Cauca

     Universidad del Cauca

     Colombia

     
  2. [2] Universidad del Valle
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 34, Nº. 2, 2016 (Ejemplar dedicado a: Revista Integración), págs. 187-206
• Idioma: español
• DOI: 10.18273/revint.v34n2-2016006
• Títulos paralelos:
  • A quasi-Newton algorithm to solve the matrix quadratic equation
• Enlaces
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• Resumen
  • español

    En este artículo proponemos un algoritmo cuasi-Newton para resolver una ecuación cuadráti a matricial, el cual reduce el costo computacional del método Newton-Schur, tradicionalmente usado para resolver dicha ecuación. Demostramos que el algoritmo propuesto es local y hasta cuadráticamente convergente. Presentamos pruebas numéricas que ratifican los resultados teóricos desarrollados.

  • English

    In this paper we propose a quasi-Newton algorithm to solve a matrix quadratic equation, which reduces the computational cost of Newton-Schur method, traditionally used to solve this equation. We show that the proposed algorithm is lo al and up to quadratically convergent. We present some numerical tests which conrfirm the theoretical results developed.

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