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A GENERALIZED THEOREM OF MIRANDA AND THE THEOREM OF NEWTON–KANTOROVICH
Numerical Functional Analysis and Optimization, 2002ABSTRACT In this paper, we discuss the theorems of Newton–Kantorovich, the Theorem of Miranda, and the relationship between them. We begin by generalizing Miranda's theorem and propose a converse. Then we show that mappings satisfying the assumptions of the Theorem of Newton–Kantorovich in a strong sense automatically satisfy those of our ...
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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, Yueqing Zhao
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Newton–Kantorovich type convergence theorem for a family of new deformed Chebyshev method
Applied Mathematics and Computation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingbiao Wu, Yueqing Zhao
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Applied Mathematics and Computation, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yueqing Zhao, Qingbiao Wu
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yueqing Zhao, Qingbiao Wu
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A note on the Kantorovich theorem for Newton iteration
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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A robust Kantorovich’s theorem on the inexact Newton method with relative residual error tolerance
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, B F Svaiter
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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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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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