A construction procedure of iterative methods with cubical convergence
Nonlinear operator equations in a Banach space, their solution by means of a parameter-based continuation method, and a Kantorovich-type convergence analysis for it are considered. The authors design new iterative methods based on a convex combination of the operators describing the well known third-order Chebyshev method and convergence acceleration of Newton's method. With the convergence result for this family of methods, an error estimate is given, too. The article is completed with examples and numerical tests.
convergence acceleration of Newton's method
scientific article; zbMATH DE number 1062206
scientific article