Newton's Method for Underdetermined Systems of Equations Under the γ-Condition

DOI10.1080/01630560701348509zbMath1120.65070OpenAlexW2008819957MaRDI QIDQ5297954

Chong Li, Jinsu He, Jin-Hua Wang

Publication date: 16 July 2007

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630560701348509

zbMATH Keywords

convergenceNewton's method\(\gamma\)-conditionSmale's point estimate theoryunderdetermined systems of equations

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items (14)

Extended Newton methods for conic inequalities: approximate solutions and the extended Smale \(\alpha\)-theory ⋮ Convergence analysis of the Gauss-Newton-type method for Lipschitz-like mappings ⋮ Extended Newton-type method and its convergence analysis for nonsmooth generalized equations ⋮ Solving inverse Pareto eigenvalue problems ⋮ Solving inverse cone-constrained eigenvalue problems ⋮ Reconstructing a matrix from a partial sampling of Pareto eigenvalues ⋮ 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 ⋮ Convergence analysis of extended Hummel-Seebeck-type method for solving variational inclusions ⋮ Smale's \(\alpha \)-theory for inexact Newton methods under the \(\gamma \)-condition ⋮ Convergence behavior of Gauss-Newton's method and extensions of the Smale point estimate theory ⋮ Quantitative Analysis for Perturbed Abstract Inequality Systems in Banach Spaces ⋮ Convergence behavior for Newton-Steffensen's method under \(\gamma\)-condition of second derivative ⋮ Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings

Cites Work

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• Convergence of Newton-like methods for singular operator equations using outer inverses
• Convergence of Newton's method and uniqueness of the solution of equations in Banach spaces. II
• Local and global behavior for algorithms of solving equations
• Newton's method for analytic systems of equations with constant rank derivatives
• Convergence and uniqueness properties of Gauss-Newton's method
• Inner, outer, and generalized inverses in banach and hilbert spaces
• The fundamental theorem of algebra and complexity theory
• Complexity of Bezout’s Theorem IV: Probability of Success; Extensions
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space
• Newton's method on Riemannian manifolds: Smale's point estimate theory under the γ-condition

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