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Note on the improvement of Newton’s method for system of nonlinear equations. (English) Zbl 1243.65058
Summary: We are concerned with the further study for a significant improvement on Newton’s iterative method proposed by the author in [Appl. Math. Comput. 112, No. 1, 75–78 (2000; Zbl 1023.65043)]. We present a natural extension and development of the improvement on Newton’s method for system of nonlinear equation. The convergence is presented and the numerical results are given to show the efficiency of the extended method for system of nonlinear equations.

MSC:
65H10 Numerical computation of solutions to systems of equations
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References:
[1] Wu, Xinyuan, A new continuation Newton-like method and its deformation, Appl. math. comput., 112, 75-78, (2000) · Zbl 1023.65043
[2] Wu, Xinyuan; Wu, Hongwei, On a class of quadratic convergence iteration formulae without derivatives, Appl. math. comput., 107, 77-80, (2000) · Zbl 1023.65042
[3] Wu, Xinyuan; Fu, Dongsheng, New high order iteration methods without employing derivatives for solving nonlinear equations, Comput. math. appl., 41, 489-495, (2001) · Zbl 0985.65047
[4] Wu, Xinyuan, A significant improvement on newton’s iterative method, Appl. math. mech.-engl., 20, 8, 924-927, (1999) · Zbl 0940.65047
[5] J. Kou, Y. Li, X. Wang, Efficient continuation Newton-like method for solving system of nonlinear equations 174 (2006) 846-853. · Zbl 1094.65049
[6] Ortega, J.M.; Rheinboldt, W.C., Iterative solution of nonlinear equations in several variables, (1970), Academic Press New York and London · Zbl 0241.65046
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