The Kantorovich Theorem for Newton's Method
From MaRDI portal
Publication:5618203
DOI10.2307/2316909zbMath0215.27404OpenAlexW4253532698MaRDI QIDQ5618203
Publication date: 1971
Published in: The American Mathematical Monthly (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2316909
Related Items (43)
Certification for polynomial systems via square subsystems ⋮ A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions ⋮ Directional \(k\)-step Newton methods in \(n\) variables and its semilocal convergence analysis ⋮ A convergence theorem for Newton-like methods in Banach spaces ⋮ Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects ⋮ Approximate Newton methods and homotopy for stationary operator equations ⋮ Weak convergence conditions for the Newton's method in Banach space using general majorizing sequences ⋮ Generalized equations and the generalized Newton method ⋮ A nonlinear shooting method and its application to nonlinear Rayleigh-Bénard convection ⋮ An efficient sinc-collocation method via the DE transformation for eighth-order boundary value problems ⋮ H∞ optimal control of unknown linear systems by adaptive dynamic programming with applications to time‐delay systems ⋮ On per-iteration complexity of high order Chebyshev methods for sparse functions with banded Hessians ⋮ Sharp error bounds for Newton's process ⋮ optimal control of unknown continuous time linear periodic systems by adaptive dynamic programming with applications to magnetic attitude control ⋮ Estimating upper bounds on the limit points of majorizing sequences for Newton's method ⋮ Extended Kantorovich theory for solving nonlinear equations with applications ⋮ Weaker conditions for the convergence of Newton's method ⋮ Extending the applicability of secant methods and nondiscrete induction ⋮ An updated version of the Kantorovich theorem for Newton's method ⋮ Recurrence relations for rational cubic methods. I: The Halley method ⋮ The majorant method in the theory of Newton-Kantorovich approximations and generalized Lipschitz conditions ⋮ Error bounds for Newton’s process derived from the Kantorovich theorem ⋮ Secant-type methods and nondiscrete induction ⋮ A parser for the interval evaluation of analytical functions and its application to engineering problems ⋮ Convergence of Stirling's method in Banach spaces ⋮ Newton's method and nonlinear boundary value problems ⋮ The Kantorovich theorem and interior point methods ⋮ A new family of high-order directions for unconstrained optimization inspired by Chebyshev and Shamanskii methods ⋮ Asymptotic Analysis and Numerical Method for Singularly Perturbed Eigenvalue Problems ⋮ Asymptotics in directed exponential random graph models with an increasing bi-degree sequence ⋮ On the convergence of inexact Newton-like methods under mild differentiability conditions ⋮ A control polygon scheme for design of planar \(C^2\) PH quintic spline curves ⋮ Reduced recurrence relations for the Chebyshev method ⋮ Recurrence relations for rational cubic methods. II: The Chebyshev method ⋮ A convergence theorem for Newton’s method in Banach spaces ⋮ Extending the applicability of Newton’s method using nondiscrete induction ⋮ Second-derivative-free variant of the Chebyshev method for nonlinear equations ⋮ Computationally efficient simultaneous policy update algorithm for nonlinearH∞state feedback control with Galerkin's method ⋮ Historical developments in convergence analysis for Newton's and Newton-like methods ⋮ The theory of Newton's method ⋮ Error bounds for Newton's iterates derived from the Kantorovich theorem ⋮ A unified derivation of several error bounds for Newton's process ⋮ A short survey on Kantorovich
This page was built for publication: The Kantorovich Theorem for Newton's Method