Gürsoy, FaikEksteen, Johannes Jacobus ArnoldiKhan, Abdul RahimKarakaya, Vatan2019-05-282019-08Gürsoy, F., Eksteen, J.J.A., Khan, A.R. et al. An iterative method and its application to stable inversion. Soft Computing (2019) 23: 7393-7406. https://doi.org/10.1007/s00500-018-3384-6.1432-7643 (print)1433-7479 (online)10.1007/s00500-018-3384-6http://hdl.handle.net/2263/69227In this paper, we study convergence and data dependence of SP and normal-S iterative methods for the class of almost contraction mappings under some mild conditions. The validity of these theoretical results is confirmed with numerical examples. It has been observed that a special case of SP iterative method, namely normal-S iterative method, performs better and so the latter is implemented in the stable inversion of nonlinear discrete time dynamical systems to yield convergence results when Picard iterative method diverges. This is also illustrated with a numerical example. Our work extends and improves upon many results existing in the literature.en© Springer-Verlag GmbH Germany, part of Springer Nature 2018. The original publication is available at : http://link.springer.comjournal/500.ConvergenceData dependencyIterative methodRate of convergenceStable inversionEngineering, built environment and information technology articles SDG-09SDG-09: Industry, innovation and infrastructureEngineering, built environment and information technology articles SDG-04SDG-04: Quality educationPostprint Article