Least change update methods for nonlinear systems with nondifferentiable terms∗
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 14 (3-4) , 405-415
- https://doi.org/10.1080/01630569308816530
Abstract
We extend the local convergence theory of least change secant update methods given by Marténez (Mathematics of Computation 55, 143-167, 1990) to nonlinear systems with nondifferentiable terms as studied by Zabrejko and Nguen (Numerical Functional Analysis and Optimization 9, 671-684, 1987), Chen and Yama-moto in a sequence of recent papers.Keywords
This publication has 12 references indexed in Scilit:
- A Family of Quasi-Newton Methods for Nonlinear Equations with Direct Secant Updates of Matrix FactorizationsSIAM Journal on Numerical Analysis, 1990
- On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable termsAnnals of the Institute of Statistical Mathematics, 1990
- Ball-convergence theorems and error estimates for certain iterative methods for nonlinear equationsJapan Journal of Applied Mathematics, 1990
- Convergence domains of certain iterative methods for solving nonlinear equationsNumerical Functional Analysis and Optimization, 1989
- A note on a posteriori error bound of zabrejko and nguen for zincenko's iterationNumerical Functional Analysis and Optimization, 1987
- An Interval Arithmetic Approach for the Construction of an Almost Globally Convergent Method for the Solution of the Nonlinear Poisson Equation on the Unit SquareSIAM Journal on Scientific and Statistical Computing, 1984
- Convergence Theorems for Least-Change Secant Update MethodsSIAM Journal on Numerical Analysis, 1981
- A characterization of superlinear convergence and its application to quasi-Newton methodsMathematics of Computation, 1974
- On the Local and Superlinear Convergence of Quasi-Newton MethodsIMA Journal of Applied Mathematics, 1973
- A class of methods for solving nonlinear simultaneous equationsMathematics of Computation, 1965