bookPart
Complexity of an Homotopy Method at the Neighbourhood of a Zero
Registro en:
9783319392288
2199-3041
Autor
Yakoubsohn, J. C.
Gutierrez, J. M.
Magreñán, Á. Alberto (1)
Institución
Resumen
This paper deals with the enlargement of the region of convergence of Newton's method for solving nonlinear equations defined in Banach spaces. We have used an homotopy method to obtain approximate zeros of the considered function. The novelty in our approach is the establishment of new convergence results based on a Lipschitz condition with a L-average for the involved operator. In particular, semilocal convergence results (Kantorovich-type results), as well as local convergence results (gamma-theory) are obtained.