Uniqueness of the solution in a Kantorovich-type theorem of Häu\ler for the Gauss-Newton Method

DOI10.1007/BF03167916zbMath0667.65053MaRDI QIDQ3819914

Tetsuro Yamamoto

Publication date: 1989

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

zbMATH Keywords

nonlinear regressionGauss-Newton methodKantorovich-type convergence theorem

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) General nonlinear regression (62J02) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10) Probabilistic methods, stochastic differential equations (65C99)

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Convergence of Newton-like methods for singular operator equations using outer inverses ⋮ Newton-like methods for solving underdetermined nonlinear equations with nondifferentiable terms ⋮ Inexact Newton-type methods ⋮ Local convergence of a secant type method for solving least squares problems ⋮ A derivative free iterative method for solving least squares problems ⋮ Newton-Type Solvers Using Outer Inverses for Singular Equations ⋮ A Convergence Analysis of Newton-Like Method for Singular Equations Using Recurrent Functions ⋮ Fixed points for operators with generalized Hölder derivative ⋮ New conditions for the convergence of Newton-like methods and applications ⋮ Historical developments in convergence analysis for Newton's and Newton-like methods

Cites Work

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• A Kantorovich-type convergence analysis for the Gauss-Newton-method
• A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
• A convergence theorem for Newton-like methods in Banach spaces
• A convergence theorem for Newton’s method in Banach spaces
• Error bounds for Newton-like methods under Kantorovich type assumptions