TY - BOOK ID - 15993391 TI - Newton’s method: an updated approach of Kantorovich’s theory AU - Ezquerro Fernández, José Antonio. AU - Hernández Verón, Miguel Ángel. PY - 2017 SN - 3319559761 3319559753 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Newton-Raphson method. KW - Method, Newton-Raphson KW - Method of tangents KW - Newton approximation method KW - Newton iterative process KW - Newton method KW - Newton-Raphson algorithm KW - Newton-Raphson formula KW - Newton-Raphson process KW - Newton's approximation method KW - Newton's method KW - Quadratically convergent Newton-Raphson process KW - Raphson method, Newton KW - -Second-order Newton-Raphson process KW - Mathematics. KW - Integral equations. KW - Operator theory. KW - Computer mathematics. KW - Operator Theory. KW - Computational Mathematics and Numerical Analysis. KW - Integral Equations. KW - Iterative methods (Mathematics) KW - Computer science KW - Equations, Integral KW - Functional equations KW - Functional analysis KW - Computer mathematics KW - Discrete mathematics KW - Electronic data processing KW - Mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:15993391 AB - 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. ER -