ON THE LOCAL CONVERGENCE OF WEIGHTED-NEWTON METHODS UNDER WEAK CONDITIONS IN BANACH SPACES.

In this paper, we consider the weighted-Newton methods developed in [18] and study their local convergence in Banach space. In the earlier study the Taylor expansion of higher order derivatives is used which may not exist or may be very expensive or impossible to compute. However, the hypotheses of present analysis are based on the first Fréchetderivative only, thereby the applicability of methods is expanded. New analysis also provides radius of convergence, error bounds and estimates on the uniqueness of the solution. Such estimates are not provided in the approaches that use Taylor expansions of higher order derivatives. Order of convergence of the methods is calculated by using computational order of convergence or approximate computational order of convergence without using higher order derivatives. Numerical tests are performed on some problems of different nature that confirm the theoretical results. [ABSTRACT FROM AUTHOR]