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A family of optimal sixteenth-order multipoint methods with a linear fraction plus a trivariate polynomial as the fourth-step weighting function. (English) Zbl 1222.65046
Summary: A new family of four-step optimal multipoint iterative methods of order sixteen for solving nonlinear equations are developed along with their convergence properties. Numerical experiments with comparison to some existing methods are demonstrated to support the underlying theory.

65H05Single nonlinear equations (numerical methods)
Full Text: DOI
[1] Bi, W.; Ren, H.; Wu, Q.: Three-step iterative methods with eighth-order convergence for solving nonlinear equations, Journal of computational and applied mathematics 225, 105-112 (2009) · Zbl 1161.65039 · doi:10.1016/j.cam.2008.07.004
[2] Bi, W.; Wu, Q.; Ren, H.: A new family of eighth-order iterative methods for solving nonlinear equations, Applied mathematics and computation 214, 236-245 (2009) · Zbl 1173.65030 · doi:10.1016/j.amc.2009.03.077
[3] Geum, Y. H.; Kim, Y. I.: A multi-parameter family of three-step eighth-order iterative methods locating a simple root, Applied mathematics and computation 215, 3375-3382 (2010) · Zbl 1183.65049 · doi:10.1016/j.amc.2009.10.030
[4] Liu, L.; Wang, X.: Eighth-order methods with high efficiency index for solving nonlinear equations, Applied mathematics and computation 215, 3449-3454 (2010) · Zbl 1183.65051 · doi:10.1016/j.amc.2009.10.040
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[8] King, R.: A family of fourth-order methods for nonlinear equations, SIAM journal on numerical analysis 10, No. 5, 876-879 (1973) · Zbl 0266.65040 · doi:10.1137/0710072
[9] Jarratt, P.: Some fourth-order multipoint iterative methods for solving equations, Mathematics of computation 20, No. 95, 434-437 (1966) · Zbl 0229.65049 · doi:10.2307/2003602
[10] Neta, B.: On a family of multipoint methods for non-linear equations, International journal of computer mathematics 9, 353-361 (1981) · Zbl 0466.65027 · doi:10.1080/00207168108803257
[11] Petković, M. S.: On a general class of multipoint root-finding methods of high computational efficiency, SIAM journal on numerical analysis 47, No. 6, 4402-4414 (2010) · Zbl 1209.65053 · doi:10.1137/090758763
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