Resolution of quadratic equations in banach spaces

Abstract

A new convergence theorem is established for the super-Halley method. This method has, in general, order three, but when it is applied to quadratic equations, its order is four.

Keywords:

• Nonlinear equations in Banach spaces
• third-order method
• Chebyshev method
• Halley Method
• super-Halley method
• convergence theorem
• error estimates