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On a class of quadratic convergence iteration formulae without derivatives. (English) Zbl 1023.65042

Summary: A class of iterative formulae without derivatives is proposed. These methods are shown to be quadratic convergence. Some numerical tests are given.

MSC:

65H05 Numerical computation of solutions to single equations
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References:

[1] A.M. Ostrowski, Solution of Equations in Eucilidean and Banach Space, 3rd ed., Academic Press, New York, 1973
[2] P. Jarratt, A review of methods for solving nonlinear algebraic equations in one variable, in: Numerical Methods for Nonlinear Algebraic Equations, Science, Gordon and Breach, London, 1970, pp. 1-26 · Zbl 0252.65039
[3] Steffensen, I.F., Remarks on iteration, Skand aktuarietidskr, 16, 64-72, (1933) · Zbl 0007.02601
[4] J.M. Ortega, W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970 · Zbl 0241.65046
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