Study of a biparametric family of iterative methods

[EN] The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the c -iterative methods and the well-known Chebyshev-Halley family. We find the analytical expressions for the fixed and critical points by solving 6-degree polynomials. We use the free critical points to get the parameter planes and, by observing them, we specify some values of (alfa, c) with clear stable and unstable behaviors.This work was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-{01,02}, P11B2011-30 of the Universitat Jaume I, and PAID-SP20120474 of the Universitat Politècnica de València.Campos, B.; Cordero Barbero, A.; Magreñán Ruiz, ÁA.; Torregrosa Sánchez, JR.; Vindel Cañas, P. (2014). Study of a biparametric family of iterative methods. Abstract and Applied Analysis. 2014. doi:10.1155/2014/141643S201