Extending the applicability of secant methods and nondiscrete induction
Nondiscrete mathematical induction is used to extend the applicability of secant methods for solving nonlinear operator equations in a Banach space setting. This approach has the following advantages over earlier works under the same information: weaker sufficient convergence conditions; tighter error bounds on the distances involved and more information on the location of the solution. Numerical examples where these results apply but earlier ones fail to solve nonlinear operator equations as well as tighter error bounds are also provided in this study.
scientific article; zbMATH DE number 6045151
scientific article