An Acceleration of Newton's Method: Super-Halley Method
Abstract¶
From a study of the convexity we give an acceleration for Newton's method and obtain a new third order method. Then we use this method for solving non-linear equations in Banach spaces, establishing conditions on convergence, existence and uniqueness of solution, as well as error estimates
Summary¶
Derives the Super-Halley method as a third-order acceleration of Newton's method using convexity arguments, then analyzes it for nonlinear equations in Banach spaces. The paper contributes convergence, existence, uniqueness, and error-estimate conditions for the accelerated iteration.
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