BIT Numerical Mathematics

, Volume 49, Issue 2, pp 325–342

New iterations of R-order four with reduced computational cost



From a one-point iterative method of R-order at least three, we construct new two-point iterations to solve nonlinear equations in Banach spaces such that the computational cost is reduced, whereas the R-order of convergence is increased to at least four.


Nonlinear equations in Banach spaces Semilocal convergence Recurrence relations A priori error estimates R-order of convergence 

Mathematics Subject Classification (2000)

45G10 47H17 65J15 


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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Mathematics and ComputationUniversity of La RiojaLogroñoSpain

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