General Study of Iterative Processes of <Emphasis Type="Italic">R</Emphasis>-Order at Least Three under Weak Convergence Conditions |
| |
Authors: | M A Hernández N Romero |
| |
Institution: | 1.Department of Mathematics and Computation,University of La Rioja,Logro?o,Spain |
| |
Abstract: | We consider a family of Newton-type iterative processes solving nonlinear equations in Banach spaces, that generalizes the
usually iterative methods of R-order at least three. The convergence of this family in Banach spaces is usually studied when the second derivative of the
operator involved is Lipschitz continuous and bounded. In this paper, we relax the first condition, assuming that ‖F″(x)−F″(y)‖≤ω(‖x−y‖), where ω is a nondecreasing continuous real function. We prove that the different R-orders of convergence that we can obtain depend on the quasihomogeneity of the function ω. We end the paper by applying the study to some nonlinear integral equations.
This work was supported by the Ministry of Science and Technology (BFM 2002-00222), the University of La Rioja (API-04/13)
and the Government of La Rioja (ACPI 2003/2004). |
| |
Keywords: | Newton-type iterative processes R-Order of convergence Semilocal convergence |
本文献已被 SpringerLink 等数据库收录! |
|