Convergence and uniqueness properties of Gauss-Newton's method

DOI10.1016/S0898-1221(04)90086-7zbMath1076.65053MaRDI QIDQ1767824

Chong Li, Wen-Hong Zhang, Xiao-qing Jin

Publication date: 8 March 2005

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

convergence ballnonlinear least squares problemuniqueness ballGauss-Newton's methodLipschitz conditions with \(L\) average

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (20)

On iterative computation of fixed points and optimization ⋮ Inexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant condition ⋮ Newton's Method for Underdetermined Systems of Equations Under the γ-Condition ⋮ Approximate Gauss-Newton methods for solving underdetermined nonlinear least squares problems ⋮ Convergence analysis of the Gauss-Newton-type method for Lipschitz-like mappings ⋮ Convergence analysis of a proximal Gauss-Newton method ⋮ Improved local convergence analysis of inexact Gauss-Newton like methods under the majorant condition in Banach spaces ⋮ Local convergence analysis of the Gauss-Newton method under a majorant condition ⋮ A Gauss-Newton method for mixed least squares-total least squares problems ⋮ The convergence analysis of inexact Gauss-Newton methods for nonlinear problems ⋮ Extending the applicability of the Gauss-Newton method under average Lipschitz-type conditions ⋮ Convergence criterion of Newton's method for singular systems with constant rank derivatives ⋮ Kantorovich's type theorems for systems of equations with constant rank derivatives ⋮ Convergence analysis of extended Hummel-Seebeck-type method for solving variational inclusions ⋮ Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition ⋮ On the solution of systems of equations with constant rank derivatives ⋮ Convergence behavior of Gauss-Newton's method and extensions of the Smale point estimate theory ⋮ Improved local convergence analysis of inexact Newton-like methods under the majorant condition ⋮ Local convergence analysis of inexact Gauss-Newton like methods under majorant condition ⋮ Improved local convergence analysis of the Gauss-Newton method under a majorant condition

Cites Work

• Convergence of Newton's method and uniqueness of the solution of equations in Banach spaces. II
• Convergence and Complexity of Newton Iteration for Operator Equations
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space
• On the Continuity of the Generalized Inverse
• Perturbation theory for pseudo-inverses
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