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

• Κύριοι συγγραφείς: Ezquerro Fernández, José Antonio (Συγγραφέας), Hernández Verón, Miguel Ángel (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.
• Σειρά: Frontiers in Mathematics,
• Θέματα: 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 analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular. 

 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.