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Potra, Florian Alexandru

An application of the induction method of V. Ptak to the study of regula falsi. (English) Zbl 0486.65038

Apl. Mat. 26, 111-120 (1981).
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scan of Zbl 0486.65038

Cited in 1 Review
Cited in 14 Documents

MSC:

65H10 Numerical computation of solutions to systems of equations

Keywords:

induction method; regula falsi; p-dimensional rate of convergence; secant method; iterative procedure

Citations:

Zbl 0323.46005; Zbl 0378.65031
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Full Text: DOI EuDML

References:

[1] M. Balazs G. Goldner: On existence of divided differences in linear spaces. Revue d’analyse numérique et de la théorie de l’approximation, 2 (1973), 5-9. · Zbl 0356.65042
[2] M. Fréchet: La notion de differentielle dans l’analyse générale. Ann. Ec. Norm. Sup, 42, (1925) 293-323. · JFM 51.0312.03
[3] T. Popoviciu: Introduction à Ia théorie des differences divisées. Bull. Math. Soc. Roum. Sci., 42 (1941), 65-78. · JFM 66.0389.01
[4] V. Pták: The rate of convergence of Newton’s process. Numer. Math., 25 (1976), 279 - 285. · Zbl 0304.65037 · doi:10.1007/BF01399416
[5] V. Pták: Nondiscrete mathematical induction and iterative existence proofs. Linear algebra and its applications 13 (1976), 233 - 238. · Zbl 0323.46005
[6] V. Pták: What should be a rate of convergence?. R. A.I. R. O. , Analyse Numérique 11,3 (1977), 279-286. · Zbl 0378.65031
[7] J. Schmidt: Eine Übertragung der Regula Falsi auf Gleichungen in Banachraum. I, II, Z. Angew. Math. Mech., 43 (1963), p. 1-8, 97-11.0. · Zbl 0115.34002 · doi:10.1002/zamm.19630430102
[8] J. Schröder: Nichtlineare Majoranten beim Verfahren der schrittweissen Näherung. Arch. Math. (Basel) 7 (1956), 471-484. · Zbl 0080.10605 · doi:10.1007/BF01899031
[9] А. С. Сергеев: О метоге хорд. Сибир. Матем. Ж. 2 (1961), 282-289. · Zbl 1160.68305 · doi:10.1147/rd.53.0183
[10] С. Улъм: Об обобщенных разделенных разностях. I, II И АН ЭССР, Физика, математика, 16 (1967) p. 13-26, 146-156. · Zbl 1103.35360 · doi:10.1103/PhysRevLett.19.1095
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