We discuss local convergence of Newton's method to a singular solution x* of the nonlinear equations F(x) = 0, for $$F:{\mathbb{R}}^n \rightarrow {\mathbb{R}}^n$$ . It is shown that an existing proof of Griewank, concerning linear convergence to a ...
In general, when a quasi-Newton method is applied to solve a system of nonlinear equations, the quasi-Newton direction is not necessarily a descent direction for the norm function. In this paper, we show that when applied to solve symmetric nonlinear ...
This paper presents a new modified Newton method for nonlinear equations. This method uses a part of elements of the Jacobian matrix to obtain the next iteration point and is refereed to as the incomplete Jacobian Newton (IJN) method. The IJN method may ...
Society for Industrial and Applied Mathematics
United States
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