Abstract
An analog of the secant method using successive approximations for an inverse operator is studied. This is a second-order method. The Newton-Kantorovich method of obtaining successive approximations for an inverse operator is a special case of the method discussed here.
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S. Yu. Ulm, “Iteration methods using successive approximations to an inverse operator,” Izv. Akad. Nauk Estonskol SSR, Ser. Fiz.-Matern. Nauk,16, No. 4, 403–411 (1967).
V. M. Chernyshenko, General Theory of Multipoint Iteration Formulas [in Russian], Articles Presented at the Interuniversity Congress of Young Mathematicians, Dnepropetrovsk (1966), pp. 19–24.
G. Schulz, “Iterative Berechnung der reziproken Matrix,” Z. Angew. Math, und Mech.,13, 57–59 (1933).
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Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 487–492, October, 1970.
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Ogneva, V.A., Cher n'yshenko, V.M. Analog of the secant method for Banach spaces. Mathematical Notes of the Academy of Sciences of the USSR 8, 742–745 (1970). https://doi.org/10.1007/BF01104375
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DOI: https://doi.org/10.1007/BF01104375