Results 81 to 90 of about 1,995 (109)

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.
openaire   +4 more sources

A variant of the Newton–Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type

Applied Mathematics and Computation, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ezquerro, J. A., González, D., Hernández, M. A.   +2 more
openaire   +4 more sources

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 ...
openaire   +3 more sources

Newton–Kantorovich type convergence theorem for a family of new deformed Chebyshev method

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Qingbiao, Zhao, Yueqing
openaire   +4 more sources

Newton–Kantorovich theorem for a family of modified Halley’s method under Hölder continuity conditions in Banach space

Applied Mathematics and Computation, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, Yueqing, Wu, Qingbiao
openaire   +4 more sources

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
openaire   +3 more sources

ON THE NEWTON–KANTOROVICH THEOREM

Analysis and Applications, 2012
The Newton–Kantorovich theorem enjoys a special status, as it is both a fundamental result in Numerical Analysis, e.g., for providing an iterative method for computing the zeros of polynomials or of systems of nonlinear equations, and a fundamental result in Nonlinear Functional Analysis, e.g., for establishing that a nonlinear equation in an infinite-
Ciarlet, Philippe G., Mardare, Cristinel
openaire   +1 more source

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
openaire   +1 more source

Solution of Tikhonov’s Motion-Separation Problem Using the Modified Newton–Kantorovich Theorem

Computational Mathematics and Mathematical Physics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Belolipetskii, A. A., Ter-Krikorov, A. M.   +1 more
openaire   +2 more sources

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
openaire   +1 more source