Results 111 to 120 of about 331,959 (146)

A Comparison of the Existence Theorems of Kantorovich and Moore

SIAM Journal on Numerical Analysis, 1980
In 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, 2018
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BARTOCCINI, BENEDETTA, Danilo Costarelli, Gianluca Vinti   +2 more
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Kantorovich’s theorem for Newton’s method on Lie groups

Journal of Zhejiang University-SCIENCE A, 2007
The 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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Shadowing orbits and Kantorovich's theorem

Numerische Mathematik, 1996
The 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 short survey on Kantorovich

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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Expanding Kantorovich’s theorem for solving generalized equations

2017
In [18], G. S. Silva considered the problem of approximating the solution of the generalized equation F(x) + Q(x) ϶ 0, (22.1) where F : D → H is a Fréchet differentiable function, H is a Hilbert space with inner product ⟨., .⟩ and corresponding norm ||.||, D ⊆ H an open set and T : H ⇉ H is set-valued and maximal monotone.
Argyros, Ioannis K, Magreñán, Á. Alberto   +1 more
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A note on the comparison of the Kantorovich and Moore theorems

Nonlinear Analysis: Theory, Methods & Applications, 1990
An affine invariant form of Moore's theorem which gives sufficient conditions for existence and uniqueness of the solution to a finite system of nonlinear algebraic equations, is given. It is also shown that the above affine invariant form of Moore's theorem is at least as effective as the affine invariant form of the Kantorovich theorem in the sense ...
Shen, Zuhe, Wolfe, M. A.
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On the existence theorems of Kantorovich, Miranda and Borsuk

2004
The theorems of Kantorovich, Miranda and Borsuk all give conditions on the existence of a zero of a nonlinear mapping. The authors concern themselves with relations between these theorems in terms of generality in the case that the mapping is finite-dimensional.
Alefeld, Götz, Frommer, A., Heindl, G., Mayer, G.   +3 more
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Kantorovich-type theorems for generalized equations

2018
To solve generalized equations of type \(0 \in f(x) + F(x)\) with \(f:X\rightarrow \mathbb R, F:X\Rightarrow Y\) , \(X,Y\) Banach spaces, \(f\) a continuous function, \(F\) a set-valued function with closed graph, \(f\) and \(F\) possibly nonsmooth, new Newton methods are given under convergence conditions of Kantorovich type, which means, that such ...
Cibulka, Radek, Dontchev, Asen L., Preininger, Jakob, Veliov, Vladimir M., Roubal, Tomáš   +4 more
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A One-Sided Version of a Theorem of Kantorovich

Numerical Functional Analysis and Optimization, 2008
Using 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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