Starlike domains of convergence for Newton's method at singularities

Abstract:

Given a solution x^* of a system of nonlinear equations f with singular Jacobian ∇f(x^*) we construct an open starlike domain R of initial points, from which Newton's method converges linearly to x^*. Under certain conditions the union of those straight lines through x^*, that do not intersect with R is shown to form a closed set of measure zero, which is necessarily disjoint from any starlike domain of convergence. The results apply to first and higher order singularities. © 1980 Springer-Verlag.

Año de publicación:

1980

Keywords:

• Subject Classifications: AMS(MOS): 65H10, CR: 5.15

Fuente:

scopus