NEW CONVERGENCE CONDITIONS OF SECANT METHODS VIA ALPHA THEORY

Recent theoretical analysis of numerical methods for solving nonlinear systems of equations is represented by alpha theory of Newton method developed Smale et al. The theory was extended to Secant method by providing convergence conditions by Yakoubsohn which the Secant method is treated as an operator defined for analytical functions. We use Secant methods as an iterative scheme with approximations, which results in new convergence conditions. We compare the two conditions and show that the new conditions represent the features of Secant method in a more precise way.