A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton–Kantorovich Iterations-II.

Autor:	Regmi, Samundra, Argyros, Ioannis K., George, Santhosh, Argyros, Michael I.
Předmět:	BOUNDARY value problems NONLINEAR equations BANACH spaces MATHEMATICS
Zdroj:	Mathematics (2227-7390); Jun2022, Vol. 10 Issue 11, p1839-1839, 12p
Abstrakt:	This article is an independently written continuation of an earlier study with the same title [Mathematics, 2022, 10, 1225] on the Newton Process (NP). This process is applied to solve nonlinear equations. The complementing features are: the smallness of the initial approximation is expressed explicitly in turns of the Lipschitz or Hölder constants and the convergence order 1 + p is shown for p ∈ (0 , 1 ]. The first feature becomes attainable by further simplifying proofs of convergence criteria. The second feature is possible by choosing a bit larger upper bound on the smallness of the initial approximation. This way, the completed convergence analysis is finer and can replace the classical one by Kantorovich and others. A two-point boundary value problem (TPBVP) is solved to complement this article. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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