Results 81 to 90 of about 171 (130)

Solution of linear equations by iterative methods in finite element analysis, February 1973 [PDF]

Kostem, Celal N., Schultchen, Erhard G.
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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
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Kantorovich theorem for variational inequalities

Applied Mathematics and Mechanics, 2004
The authors consider the known Newton method for variational inequalities and establish its local convergence properties. They specialize some estimates which determine the convergence neighborhood and can be computed explicitly.
Wang, Zhengyu, Shen, Zuhe
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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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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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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 Tarski–Kantorovich theorem for correspondences

Journal of Mathematical Economics
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Łukasz Balbus, Wojciech Olszewski, Kevin Reffett, Łukasz Woźny   +3 more
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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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The Kantorovich Theorem and interior point methods

Mathematical Programming, 2004
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Converse theorems for multidimensional Kantorovich operators

Analysis Mathematica, 1993
The author devotes most of the paper to a detailed treatment of direct and inverse theorems for Kantorovich type operators \(K_ n\) defined on \(L_ p(S)\) where \(S\) is the triangle \(\{(x,y): x,y\geq 0,\;x+ y\leq 1\}\) by \[ K_ n(f,x,y)= \sum_{k+ m\leq n} {n\choose k}{n-k\choose m} x^ k y^ m(1- x- y)^{n-k-m} 2(n+1)^ 2\iint_{\Delta_{k,m}} f(s,t)ds dt,
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