A quasi-Gauss-Newton method for solving nonlinear algebraic equations

DOI10.1016/0898-1221(93)90211-DzbMath0788.65060OpenAlexW2075959309MaRDI QIDQ1203697

H. Wang, Reginald P. Tewarson

Publication date: 22 February 1993

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

Full work available at URL: https://doi.org/10.1016/0898-1221(93)90211-d

zbMATH Keywords

system of nonlinear equationsnormal equationstest problemscomputational resultsill-conditioningQR factorizationGauss-Newton methodBroyden updateCholesky factorization updaterank-one quasi-Newton method

Mathematics Subject Classification ID

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

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Uses Software

• minpack
• GQTPAR

Cites Work

• A unified derivation of quasi-Newton methods for solving non-sparse and sparse nonlinear equations
• Computing a Trust Region Step
• A Family of Trust-Region-Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties
• Testing Unconstrained Optimization Software
• An Evaluation of Mathematical Software That Solves Systems of Nonlinear Equations
• On the Global Convergence of Broyden's Method
• Quasi-Newton Methods, Motivation and Theory
• Use of Smoothing and Damping Techniques in the Solution of Nonlinear Equations
• An Estimate for the Condition Number of a Matrix
• The Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization
• On the Local and Superlinear Convergence of Quasi-Newton Methods
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• Methods for Modifying Matrix Factorizations
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• Quasi-Newton Methods for Unconstrained Optimization
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