Numerical experience with Newton-like methods for nonlinear algebraic systems

DOI10.1007/BF02684472zbMath0866.65033MaRDI QIDQ2365380

Yanyan Li

Publication date: 27 July 1997

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

convergencerobustnessnumerical testsquasi-Newton methodsbasins of attractionABS methods

Mathematics Subject Classification ID

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

Related Items (16)

A multi-iterate method to solve systems of nonlinear equations ⋮ A globally convergent hybrid conjugate gradient method and its numerical behaviors ⋮ Solving polynomial systems using a fast adaptive back propagation-type neural network algorithm ⋮ Practical quasi-Newton algorithms for singular nonlinear systems ⋮ Some modifications of Newton's method for solving systems of equations ⋮ Dai-Kou type conjugate gradient methods with a line search only using gradient ⋮ A nonmonotone Jacobian smoothing inexact Newton method for NCP ⋮ Smoothing Levenberg-Marquardt method for general nonlinear complementarity problems under local error bound ⋮ A Levenberg-Marquardt method for nonlinear complementarity problems based on nonmonotone trust region and line search techniques ⋮ On the final steps of Newton and higher order methods ⋮ Jacobian smoothing Brown's method for NCP ⋮ A new smoothing quasi-Newton method for nonlinear complementarity problems ⋮ 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 ⋮ A numerical study on large-scale nonlinear solvers ⋮ Globally convergent Jacobian smoothing inexact Newton methods for NCP ⋮ A new class of neural networks for NCPs using smooth perturbations of the natural residual function

Cites Work

• A quasi-Newton method with modification of one column per iteration
• On the monotone convergence of Newton's method
• On the closed form solution of Troesch's problem
• A significant example to test method for solving systems of nonlinear equations
• Numerical Solution of Large Sets of Algebraic Nonlinear Equations
• A Class of Methods for Solving Nonlinear Simultaneous Equations
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