A FAMILY OF NEWTON TYPE ITERATIVE PROCESSES .
M. A. Hernández & M. A. Salanova
Universidad de La Rioja . Dpto. de Matemáticas .
Edificio de Magisterio . C/ Luis de Ulloa s/n .
26001 . LOGROŃO . SPAIN .
In this paper, we define an index of the convexity measure by
means of the logarithmic operator . As an application , we study the
influence of the convexity on Newton method for solving nonlinear
equations. Then we define a family of Newton type iterative processes t o
solve a complex or scalar nonlinear equation, we can always apply an
iterative process of this family faster than Newton method .
Classification A.M.S. 1985 . : 65 H 05 , 26 A 51
C.R. CATEGORIES : 5.1 , 5.15
Keywords : Nonlinear equations . Iterative processes . Optimization .
1. Introduction .
We begin this paper defining an index of the convexity measure for a
function h at each point . We prove that it is a good measure of the