In this paper, we present a new secant-like method for solving nonlinear equations. Analysis of the convergence shows that the asymptotic convergence order of this method is 1 + โ 3. Some numerical results are given to demonstrate its efficiency.
A modified secant method for semismooth equations
โ Scribed by S. Amat; S. Busquier
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 302 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Symmetric rank-one (SR1) is one of the competitive formulas among the quasi-Newton (QN) methods. In this paper, we propose some modified SR1 updates based on the modified secant equations, which use both gradient and function information. Furthermore, to avoid the loss of positive definiteness and z
In this paper, a new method for solving nonlinear equations f(x) = 0 is presented. In many literatures the derivatives are used, but the new method does not use the derivatives. Like the method of secant, the first derivative is replaced with a finite difference in this new method. The new method co
In this paper, some semismooth methods are considered to solve a nonsmooth equation which can arise from a discrete version of the well-known Hamilton-Jacobi-Bellman equation. By using the slant differentiability introduced by Chen, Nashed and Qi in 2000, a semismooth Newton method is proposed. The