TY  - BOOK
AU  - Ezquerro Fernández,José Antonio
AU  - Hernández Verón,Miguel Ángel
ED  - SpringerLink (Online service)
TI  - Newton’s Method: an Updated Approach of Kantorovich’s Theory
T2  - Frontiers in Mathematics,
SN  - 9783319559766
AV  - QA329-329.9 
U1  - 515.724 23
PY  - 2017///
CY  - Cham
PB  - Springer International Publishing, Imprint: Birkhäuser
KW  - Operator theory
KW  - Computer mathematics
KW  - Integral equations
KW  - Operator Theory
KW  - Computational Mathematics and Numerical Analysis
KW  - Integral Equations
N1  - 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; Available to subscribing member institutions only. Доступно лише організаціям членам підписки
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-55976-6
ER  -