Convergence properties of the Broyden-like method for mixed linear-nonlinear systems of equations

DOI10.1007/s11075-020-01060-yzbMath1486.65050OpenAlexW3126627953MaRDI QIDQ820733

Florian Mannel

Publication date: 27 September 2021

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-020-01060-y

zbMATH Keywords

quasi-Newton methodsBroyden's methodBroyden-like methodconvergence of Broyden-like matricesuniform linear independence

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10)

Related Items

On the order of convergence of Broyden's method. Faster convergence on mixed linear-nonlinear systems of equations and a conjecture on the q-order

Cites Work

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• The convergence of matrices generated by rank-2 methods from the restricted \(\beta\)-class of Broyden
• Convergence of quasi-Newton matrices generated by the symmetric rank one update
• The convergence of quasi-Newton matrices generated by the self-scaling symmetric rank one update
• A note on the convergence of the secant method for simple and multiple roots
• Practical quasi-Newton methods for solving nonlinear systems
• Convergence of Broyden-like matrix
• Broyden updating, the good and the bad!
• Broyden's quasi-Newton methods for a nonlinear system of equations and unconstrained optimization: a review and open problems
• The convergence of variable metric matrices in unconstrained optimization
• Convergence Rates of Quasi-Newton Algorithms for Some Nonsmooth Optimization Problems
• How bad are the BFGS and DFP methods when the objective function is quadratic?
• Broyden’s Method for a Class of Problems Having Singular Jacobian at the Root
• Some Convergence Properties of Broyden’s Method
• On the Superlinear Convergence of the Secant Method
• On the Global Convergence of Broyden's Method
• Quasi-Newton Methods, Motivation and Theory
• Extra updates for the bfgs method^∗
• A derivative-free line search and global convergence of Broyden-like method for nonlinear equations
• A Theoretical and Experimental Study of the Symmetric Rank-One Update
• On the Local and Superlinear Convergence of Quasi-Newton Methods
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• Why Broyden’s Nonsymmetric Method Terminates on Linear Equations
• Iterative Solution of Nonlinear Equations in Several Variables
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• A New Algorithm for Unconstrained Optimization