Sobre la convergencia de un método secante
para ecuaciones matriciales no lineales

MAURICIO MACÍAS C.^{a *}, HÉCTOR J. MARTÍNEZ^b, ROSANA PÉREZ^a

^aUniversidad del Cauca, Departamento de Matemáticas, Popayán, Colombia.

^b Universidad del Valle, Departamento de Matemáticas, Cali, Colombia.

Resumen. En este artículo desarrollamos una teoría general de convergencia de un método secante para resolver ecuaciones matriciales no lineales. Además, presentamos condiciones suficientes para que este método proporcione un algoritmo local y superlinealmente convergente.

Palabras claves: Función matricial, operador de Fréchet, Fréchet diferenciable, método secante, ecuación matricial no lineal, convergencia superlineal.
MSC2010: 65F10, 65N22, 65H10, 49M15, 49M37, 90C53.

Abstract. In this paper we develop a general theory of convergence of a secant method to solve nonlinear matrix equations. In addition, we give sufficient conditions in order to this method provide a local and superlinearly convergent algorithm.

Keywords: Matrix function, Fréchet operator, Fréchet differentiable, secant method, nonlinear matrix equation, superlinear convergence.

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*E-mail: mauromac@unicauca.edu.co.
Recibido: 20 de marzo de 2014, Aceptado: 13 de agosto de 2014.
Para citar este artículo: E.M. Macías, H.J. Martínez, R. Pérez, Sobre la convergencia de un método secante
para ecuaciones matriciales no lineales, Rev. Integr. Temas Mat. 32 (2014), no. 2, 181-197.