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A composite third order Newton-Steffensen method for solving nonlinear equations. (English) Zbl 1084.65054
The author presents a third order method for local refinement of roots of single nonlinear equations, which is a combination of the standard Newton iteration formula and the Stephenson formula. The method could be useful to calculate zeros of functions with large values that may otherwise cause overflow.

65H05Single nonlinear equations (numerical methods)
Full Text: DOI
[1] Amat, S.; Busquier, S.; Guti√©rrez, J. M.: Geometric constructions of iteration functions to solve nonlinear equations. J. comput. Appl. math. 157, 197-205 (2003) · Zbl 1024.65040
[2] Dennis, J. E.; Schnable, R. B.: Numerical methods for unconstrained optimization and nonlinear equations. (1983)
[3] Jarratt, P.: A review of methods for solving nonlinear algebraic equations. (1970) · Zbl 0252.65039
[4] Johnson, L. W.; Riess, R. D.: Numerical analysis. (1977) · Zbl 0412.65001
[5] Ostrowski, A. M.: Solution of equations in Euclidean and Banach space. (1973) · Zbl 0304.65002
[6] Steffensen, I. F.: Remarks on iteration. Skand. aktuarietidskr. 16, 64-72 (1933) · Zbl 0007.02601