Geodesic
Error bounds for the secant method
Mathematica slovaca, Tome 41 (1991) no. 1, pp. 69-82

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Classification : 47J25, 65J15 
Argyros, Ioannis K. Error bounds for the secant method. Mathematica slovaca, Tome 41 (1991) no. 1, pp. 69-82. http://geodesic.mathdoc.fr/item/MASLO_1991_41_1_a9/
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[1] ARGYROS I. K.: Newton-like methods under mild differentiability conditions with error analysis. Bull. Austral. Math. Soc. Vol. 37, 2, 1987, 131-147. | MR

[2] ARGYROS I. K.: On Newton's method and nondiscrete mathematical induction. Bull. Austral. Math. Soc. Vol. 38, 1988, 131-140. | MR | Zbl

[3] DENNIS J. E.: Toward a unified convergence theory for Newton-like methods. In: Nonlinear Functional Analysis and Applications, L. B. Rail, Ed., Academic Press, New York, 1971. | MR | Zbl

[4] GRAGG W. B., TAPIA R. A.: Optimal error bounds for the Newton-Kantorovich theorem. S.I.A.M. J. Numer. Anal. 11, 1, 1974, 10-13. | MR | Zbl

[5] OSTROWSKI M. A.: Solution of equations in Euclidian and Banach spaces. Academic Press, New York, 1973. | MR

[6] POTRA F. A., PTÁK V.: Sharp error bounds for Newton's process. Numer. Math. 34, 1980, 63-72. | MR | Zbl

[7] POTRA F. A.: An error analysis for the Secant method. Numer. Math. 38, 1982, 427-445. | MR | Zbl

[8] POTRA F. A.: Sharp error bounds for a class of Newton-like methods. Libertas Mathematica 5, 1985, 71-84. | MR | Zbl

[9] POTRA F. A., PTÁK V.: Nondiscrete induction and iterative processes. Pitman Publ. Boston, 1984. | MR | Zbl

[10] PTÁK V.: Nondiscrete mathematical induction and iterative existence proofs. Linear Algebra Appl. 13, 1976, 223-236. | MR

[11] SCHMIDT J. W.: Regula-Falsi Verfahren mit konsistenter Steigung und Majoranten Prinzip. Period. Math. Hungar. 5, 3, 1974, 187-193. | MR

[12] SERGEEV A. S.: On the method of chords Sibirsk. Mat. Z. 2, 1961, 282-289. | MR