Accelerated methods of order 2p for systems of nonlinear equations

  • Authors:

  • Alicia Cordero;José L. Hueso;Eulalia Martínez;Juan R. Torregrosa

  • Affiliations:

  • Instituto de Matemática Multidisciplinar, Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain;Instituto de Matemática Multidisciplinar, Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain;Instituto de Matemática Multidisciplinar, Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain;Instituto de Matemática Multidisciplinar, Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

We present a new iterative method of order of convergence 5, for solving nonlinear systems, by composing the Midpoint method with Newton's method and using an approximation for the Jacobian matrix in order to reduce the required number of functional evaluations per iteration. In addition, we compare the efficiency index of these methods with that of Newton's method and present several numerical tests, which confirm the theoretical results and allow us to compare these variants with Newton's method.