Abstract
We develop an eighth order family of methods, consisting of three steps and three parameters, for solving nonlinear equations. Per iteration the methods require four evaluations (three function evaluations and one evaluation of the first derivative). Convergence analysis shows that the family is eighth-order convergent which is also substantiated through the numerical work. Computational results ascertain that family of methods are efficient and demonstrate equal or better performance as compared with other well known methods.
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This work was dedicated to Professor Gilbert Strang.
The work was supported by the Norwegian Research Council of Science and the Humanities.
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Khattri, S.K. Optimal Eighth Order Iterative Methods. Math.Comput.Sci. 5, 237–243 (2011). https://doi.org/10.1007/s11786-011-0064-7
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DOI: https://doi.org/10.1007/s11786-011-0064-7