Abstract It is well known that the Newton method may not converge when initial guess does belong to a specific quadratic convergence region. We propose family of new variants with potential advantage having larger region as more desirable properties near solution. prove family, and provide bounds for asymptotic error constant. illustrate advantages methods by means test problems, including two ...

The local superlinear convergence of the generalized Newton method for solving systems of nonsmooth equations has been proved by Qi and Sun under the semismooth condition and nonsingularity of the generalized Jacobian at the solution. Unlike the Newton method for systems of smooth equations, globalization of the generalized Newton method seems dif-cult to achieve in general. However, we show th...

We develop general approximate Newton methods for solving Lipschitz continuous equations by replacing the iteration matrix with a consistently approximated Jacobian, thereby reducing the computation in the generalized Newton method. Locally superlinear convergence results are presented under moderate assumptions. To construct a consistently approximated Jacobian, we introduce two main methods: ...

for the nonlinear analysis of structures using the well known newton-raphson method, the tangent stiffness matrices of the elements must be constructed in each iteration. due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the newton-raphson method to reduce the cost and time required by the analysis. in this paper, a ...