Historical developments in convergence analysis for Newton's and Newton-like methods

DOI10.1016/S0377-0427(00)00417-9zbMath0965.65079WikidataQ126574527 ScholiaQ126574527MaRDI QIDQ1593810

Tetsuro Yamamoto

Publication date: 2 August 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergenceerror estimatesbibliographyBanach spacenonlinear operator equationNewton-type methodsChebyshev's methodHalley methodhistorical developments

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) History of numerical analysis (65-03)

Related Items (46)

On the Halley class of methods for unconstrainedoptimization problems ⋮ Newton-homotopy analysis method for nonlinear equations ⋮ On the domain of starting points of Newton's method under center Lipschitz conditions ⋮ Nonlinear stochastic programming-with a case study in continuous switching ⋮ Convergence of a two-step iterative method for nondifferentiable operators in Banach spaces ⋮ On the convergence of an inexact Newton-type method ⋮ New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems ⋮ An iterative method for solving nonlinear equations ⋮ Sparse solutions of optimal control via Newton method for under-determined systems ⋮ Practical quasi-Newton algorithms for singular nonlinear systems ⋮ Analysis of a regularized Bingham model with pressure-dependent yield stress ⋮ On the complexity of a unified convergence analysis for iterative methods ⋮ On per-iteration complexity of high order Chebyshev methods for sparse functions with banded Hessians ⋮ Metrically regular vector field and iterative processes for generalized equations in Hadamard manifolds ⋮ The convergence analysis of inexact Gauss-Newton methods for nonlinear problems ⋮ Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations ⋮ Extended Kantorovich theory for solving nonlinear equations with applications ⋮ The convergence of the perturbed Newton method and its application for ill-conditioned problems ⋮ A method to find all the roots of the system of nonlinear algebraic equations based on the Krawczyk operator ⋮ On the semilocal convergence of Newton-Kantorovich method under center-Lipschitz conditions ⋮ Global existence of real roots and random Newton flow algorithm for nonlinear system of equations ⋮ On diagonally structured problems in unconstrained optimization using an inexact super Halley method ⋮ The genesis and early developments of Aitken's process, Shanks' transformation, the \(\varepsilon\)-algorithm, and related fixed point methods ⋮ The Newton-Kantorovich approximations for nonlinear singular integral equations with shift ⋮ Quasilinearization numerical scheme for fully nonlinear parabolic problems with applications in models of mathematical finance ⋮ A Hessian-free Newton-Raphson method for the configuration of physics systems featured by numerically asymmetric force field ⋮ A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions ⋮ Iterative methods for ill-conditioned roots ⋮ On some cubic convergence iterative formulae without derivatives for solving nonlinear equations ⋮ A family of methods for solving nonlinear equations ⋮ Newton-Kantorovitch method for decoupled forward-backward stochastic differential equations ⋮ Several new third-order iterative methods for solving nonlinear equations ⋮ The Kantorovich theorem and interior point methods ⋮ Estimates of majorizing sequences in the Newton-Kantorovich method: a further improvement ⋮ A method for solving nonlinear equations ⋮ Concerning the ``terra incognita between convergence regions of two Newton methods ⋮ Newton's method's basins of attraction revisited ⋮ Newton–Kantorovich Approximations When the Derivative Is Hölderian: Old and New Results ⋮ Verified error bounds for singular solutions of nonlinear systems ⋮ On the complexity of choosing majorizing sequences for iterative procedures ⋮ Estimates of Majorizing Sequences in the Newton–Kantorovich Method ⋮ Complexity of an Homotopy Method at the Neighbourhood of a Zero ⋮ Distance regression by Gauss-Newton-type methods and iteratively re-weighted least-squares ⋮ Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains ⋮ Convergence of Gauss-Newton's method and uniqueness of the solution ⋮ New versions of Newton method: step-size choice, convergence domain and under-determined equations

Uses Software

• KELLEY

Cites Work

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