On the secant method and nondiscrete mathematical induction

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  • Ioannis K. Argyros New Mexico, USA
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References

Harold T. Davis, Introduction to nonlinear differential and integral equations. Dover Publications, Inc., New York 1962 xv+566 pp., MR0181773.

L. V. Kantorovich, G. P. Akilov, G. P. Functional analysis in normed spaces. Translated from the Russian by D. E. Brown. Edited by A. P. Robertson. International Series of Monographs in Pure and Applied Mathematics, Vol. 46 The Macmillan Co., New York 1964 xiii+771 pp., MR0213845.

F. A. Potra, V. Pták, V. Nondiscrete induction and iterative processes. Research Notes in Mathematics, 103. Pitman (Advanced Publishing Program), Boston, MA, 1984. vii+207 pp., MR0754338, ISBN: 0-273-08627-8.

F. A. Potra, An error analysis for the secant method. Numer. Math. 38 (1981/82), no. 3, 427-445, MR0654108, https://doi.org/10.1007/bf01396443

Rheinboldt, Werner C. Numerical analysis of parametrized nonlinear equations. University of Arkansas Lecture Notes in the Mathematical Sciences, 7. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1986. xi+299 pp., ISBN: 0-471-88814-1, MR0815107.

W. C. Rheinboldt, A unified convergence theory for a class of iterative processes. SIAM J. Numer. Anal. 5 1968, 42-63, MR0225468, https://doi.org/10.1137/0705003

J. M. Ortega, W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables. Academic Press, New York-London 1970 xx+572 pp., MR0273810, https://doi.org/10.1002/zamm.19720520813

Vlastimil Pták, Nondiscrete mathematical induction. General topology and its relations to modern analysis and algebra, IV (Proc. Fourth Prague Topological Sympos., Prague, 1976), Part A, pp. 166-178. Lecture Notes in Math., Vol. 609, Springer, Berlin, 1977, MR0487618, https://doi.org/10.1007/bfb0068681

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Published

1989-02-01

How to Cite

Argyros, I. K. (1989). On the secant method and nondiscrete mathematical induction. Anal. Numér. Théor. Approx., 18(1), 27–36. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1989-vol18-no1-art4

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