Results 61 to 70 of about 1,971 (87)

Optimal Error Bounds for the Newton–Kantorovich Theorem

SIAM Journal on Numerical Analysis, 1974
Best possible upper and lower bounds for the error in Newton’s method are established under the hypotheses of the Kantorovich theorem.
Gragg, W. B., Tapia, R. A.
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A variant of the Newton–Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type

Applied Mathematics and Computation, 2012
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Ezquerro, J. A., González, D., Hernández, M. A.   +2 more
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A GENERALIZED THEOREM OF MIRANDA AND THE THEOREM OF NEWTON–KANTOROVICH

Numerical Functional Analysis and Optimization, 2002
ABSTRACT 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, 2006
Under 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.
Wu, Qingbiao, Zhao, Yueqing
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Newton–Kantorovich theorem for a family of modified Halley’s method under Hölder continuity conditions in Banach space

Applied Mathematics and Computation, 2008
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Zhao, Yueqing, Wu, Qingbiao
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The Newton-Kantorovich Theorem

2020
Solving 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, Miguel Ángel Hernández Verón   +1 more
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Solution of Tikhonov’s Motion-Separation Problem Using the Modified Newton–Kantorovich Theorem

Computational Mathematics and Mathematical Physics, 2018
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Belolipetskii, A. A., Ter-Krikorov, A. M.   +1 more
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Newton–Kantorovich type convergence theorem for a family of new deformed Chebyshev method

Applied Mathematics and Computation, 2007
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Wu, Qingbiao, Zhao, Yueqing
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A Modification of the Lipschitz Condition in the Newton–Kantorovich Theorem

Zeitschrift für Analysis und ihre Anwendungen, 2016
We 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, Miguel Ángel Hernández-Verón   +1 more
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Newton–Kantorovich Convergence Theorem of a Modified Newton’s Method Under the Gamma-Condition in a Banach Space

Journal of Optimization Theory and Applications, 2012
The authors study the semilocal convergence of the modified Newton's method having third-order convergence. A Newton-Kantorovich convergence theorem is established for the modified Newton's method under the gamma-condition in a Banach space to solve nonlinear equations.
Khan, Y., Chen, M., Wu, Q., Yildirim, A.
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