Practical Quasi-Newton algorithms for singular nonlinear systems

Authors:
Sandra Buhmiler;Nataša Krejić;Zorana Lužanin
Affiliations:
Department of Mathematics, Faculty of Engineering, University of Novi Sad, Novi Sad, Serbia 21000;Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Novi Sad, Serbia 21000;Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Novi Sad, Serbia 21000
Venue:
Numerical Algorithms
Year:
2010

Citing 15
Cited 1

A Shamanskii-Like acceleration scheme for nonlinear equations at singular roots

Mathematics of Computation
Inexact trust region method for large sparse systems of nonlinear equations

Journal of Optimization Theory and Applications
Local convergence analysis of tensor methods for nonlinear equations

Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
Qualitative Analysis of Newton's Flow

SIAM Journal on Numerical Analysis
Numerical experience with Newton-like methods for nonlinear algebraic systems

Computing
Tensor Methods for Large, Sparse Nonlinear Least Squares Problems

SIAM Journal on Scientific Computing
Historical developments in convergence analysis for Newton's and Newton-like methods

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Practical quasi-Newton methods for solving nonlinear systems

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Discretization of implicit ODEs for singular root-finding problems

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Sequential estimation techniques for quasi-newton algorithms.

Sequential estimation techniques for quasi-newton algorithms.
Inverse q-columns updating methods for solving nonlinear systems of equations

Journal of Computational and Applied Mathematics
The Continuous Newton--Raphson Method Can Look Ahead

SIAM Journal on Optimization
On the Relationship between the Convergence Rates of Iterative and Continuous Processes

SIAM Journal on Optimization
A new smoothing quasi-Newton method for nonlinear complementarity problems

Journal of Computational and Applied Mathematics
Newton's method for singular nonlinear equations using approximate left and right nullspaces of the Jacobian

Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing

Two derivative-free projection approaches for systems of large-scale nonlinear monotone equations

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

Quasi-Newton methods for solving singular systems of nonlinear equations are considered in this paper. Singular roots cause a number of problems in implementation of iterative methods and in general deteriorate the rate of convergence. We propose two modifications of QN methods based on Newton's and Shamanski's method for singular problems. The proposed algorithms belong to the class of two-step iterations. Influence of iterative rule for matrix updates and the choice of parameters that keep iterative sequence within convergence region are empirically analyzed and some conclusions are obtained.