How to apply Newton's method to operators with unbounded second derivative

Abstract:

The problem of finding the roots of a nonlinear equation has a long history. Although some nonlinear equations can be solved analytically, numerical approximations of the roots can be normally wanted. Moreover, since it is usually difficult or impossible to obtain an exact root of a nonlinear equation, we usually have to be satisfied with approximating the root numerically. To do this, we habitually approximate the root by iterative methods, which provide a sequence of approximations, from one or several initial approximations, that converges to the root of the nonlinear equation. © 2011 American Institute of Physics.

Año de publicación:

2011

Keywords:

• Kantorovich's conditions
• Newton's method
• semilocal convergence
• majorizing sequences

Fuente:

scopus