Newton’s Method: an Updated Approach of Kantorovich’s Theory

• Main Authors: Ezquerro Fernández, José Antonio (Author), Hernández Verón, Miguel Ángel (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.
• Series: Frontiers in Mathematics,
• Subjects: Mathematics.; Integral equations.; Operator theory.; Computer mathematics.; Operator Theory.; Computational Mathematics and Numerical Analysis.; Integral Equations.

This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional...

Table of Contents:

• The classic theory of Kantorovich
• Convergence conditions on the second derivative of the operator
• Convergence conditions on the k-th derivative of the operator
• Convergence conditions on the first derivative of the operator.