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A Newton–Kantorovich convergence theorem for the inverse-free Jarratt method in Banach space
Applied Mathematics and Computation, 2006Under weak conditions, we establish a Newton-Kantorovich type convergence theorem of the inverse-free Jarratt method in Banach space which is used to solve a nonlinear operator equation. Finally, some examples are provided to show the applicability of our theorem.
Qingbiao Wu
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Applied Mathematics and Computation, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingbiao Wu
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingbiao Wu
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A note on the Kantorovich theorem for Newton iteration [PDF]
Journal of Computational and Applied Mathematics, 1993 In this paper, a new theorem for the Newton method convergence is obtained. Its condition is different from that of the Kantorovich theorem and therefore it has theoretical and practical ...
Zhengda, Huang
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The Newton-Kantorovich Theorem
2020Solving nonlinear equations is one of the mathematical problems that is frequently encountered in diverse scientific disciplines. Thus, with the notation $$\displaystyle f(x)=0, $$ we include the problem of finding unknown quantity x, which can be a real or complex number, a vector, a function, etc., from data provided by the function f, which ...
José Antonio Ezquerro Fernández +1 more
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A Modification of the Lipschitz Condition in the Newton–Kantorovich Theorem
Zeitschrift für Analysis und ihre Anwendungen, 2016We analyse the semilocal convergence of Newton’s method in Banach spaces under a modification of the classic Lipschitz condition on the first derivative of the operator involved in Kantorovich’s theory. For this, we use a technique based on recurrence relations instead of the well-known majorant principle of Kantorovich.
José Antonio Ezquerro +1 more
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A robust Kantorovich’s theorem on the inexact Newton method with relative residual error tolerance [PDF]
Journal of Complexity, 2012 We prove that under semi-local assumptions, the inexact Newton method with a fixed relative residual error tolerance converges Q-linearly to a zero of the nonlinear operator under consideration.
O P Ferreira
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Solution of Tikhonov’s Motion-Separation Problem Using the Modified Newton–Kantorovich Theorem
Computational Mathematics and Mathematical Physics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Belolipetskii, A. A. +1 more
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