New Family of Iterative Methods with High Order of Convergence for Solving Nonlinear Systems

  • Alicia Cordero
  • Juan R. Torregrosa
  • María P. Vassileva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)


In this paper we present and analyze a set of predictor-corrector iterative methods with increasing order of convergence, for solving systems of nonlinear equations. Our aim is to achieve high order of convergence with few Jacobian and/or functional evaluations. On the other hand, by applying the pseudocomposition technique on each proposed scheme we get to increase their order of convergence, obtaining new high-order and efficient methods. We use the classical efficiency index in order to compare the obtained schemes and make some numerical test.


Nonlinear systems Iterative methods Jacobian matrix Convergence order Efficiency index 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alicia Cordero
    • 1
  • Juan R. Torregrosa
    • 1
  • María P. Vassileva
    • 2
  1. 1.Instituto de Matemática MultidisciplinarUniversitat Politècnica de ValènciaValenciaEspaña
  2. 2.Instituto Tecnológico de Santo Domingo (INTEC)República Dominicana

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