Results 131 to 140 of about 336 (171)
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ON THE NEWTON–KANTOROVICH THEOREM
Analysis and Applications, 2012The 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
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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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The Kantorovich Theorem and interior point methods
Mathematical Programming, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Kantorovich’s theorem for Newton’s method on Lie groups
Journal of Zhejiang University-SCIENCE A, 2007The aim of the paper is to study Newton's method for solving the equation \(f(x)= 0\), with \(f\) being a map from a Lie group to its corresponding algebra. Under a classical Lipschitz's condition, the convergence criterion of Newton's method independent of affine connections is established and the radius of the convergence ball is obtained.
Wang, Jin-Hua, Li, Chong
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Optimal Error Bounds for the Newton–Kantorovich Theorem
SIAM Journal on Numerical Analysis, 1974Best 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 Comparison of the Existence Theorems of Kantorovich and Moore
SIAM Journal on Numerical Analysis, 1980In order to be useful, an approximate solution y of a nonlinear system of equations $f(x) = 0$ in $R^n $ must be close to a solution $x^ * $ of the system. Two theorems which can be used computationally to establish the existence of $x^ * $ and obtain bounds for the error vector $y - x^ * $ are the 1948 result of L. V. Kantorovich and the 1977 interval
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Extension of Saturation Theorems for the Sampling Kantorovich Operators
Complex Analysis and Operator Theory, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Benedetta Bartoccini +2 more
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ACM Communications in Computer Algebra, 2016
We survey influential quantitative results on the convergence of the Newton iterator towards simple roots of continuously differentiable maps defined over Banach spaces. We present a general statement of Kantorovich's theorem, with a concise proof from scratch, dedicated to wide audience. From it, we quickly recover known results, and gather historical
Grégoire Lecerf, Joelle Saadé
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We survey influential quantitative results on the convergence of the Newton iterator towards simple roots of continuously differentiable maps defined over Banach spaces. We present a general statement of Kantorovich's theorem, with a concise proof from scratch, dedicated to wide audience. From it, we quickly recover known results, and gather historical
Grégoire Lecerf, Joelle Saadé
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Shadowing orbits and Kantorovich's theorem
Numerische Mathematik, 1996The author points out the close connection between Kantorovich's theorem on convergence of Newton's method and the existence of a finite shadowing orbit of a given pseudo-orbit. This paper clarifies some results that are already known and simplifies their proofs.
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A One-Sided Version of a Theorem of Kantorovich
Numerical Functional Analysis and Optimization, 2008Using elementary differential inequality methods, we prove an improvement of a theorem of Kantorovich concerning solutions of nonlinear equations in Banach spaces.
Gerd Herzog, Roland Lemmert
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