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A simplified proof of the Kantorovich theorem for solving equations using telescopic series. (English) Zbl 1399.65120

Summary: We extend the applicability of the Kantorovich theorem (KT) for solving nonlinear equations using Newton-Kantorovich method in a Banach space setting. Under the same information but using elementary scalar telescopic majorizing series, we provide a simpler proof for the (KT) I. Argyros [Studies in Computational Mathematics 15. Amsterdam: Elsevier, xv, 487 p. (2007; Zbl 1147.65313)]; L. V. Kantorovich and G. P. Akilov [Oxford etc.: Pergamon Press. XIV, 589 p. (1982; Zbl 0484.46003)]. Our results provide at least as precise information on the location of the solution. Numerical examples are also provided in this study.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
65G99 Error analysis and interval analysis
47H99 Nonlinear operators and their properties
49M15 Newton-type methods
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