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Newton's methodan updated approach o...

Ezquerro Fernandez, Jose Antonio.

Newton's methodan updated approach of Kantorovich's theory /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Newton's methodby Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron.
其他題名:	an updated approach of Kantorovich's theory /
作者:	Ezquerro Fernandez, Jose Antonio.
其他作者:	Hernandez Veron, Miguel Angel.
出版者:	Cham :Springer International Publishing :2017.
面頁冊數:	xii, 166 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Newton-Raphson method.
電子資源:	http://dx.doi.org/10.1007/978-3-319-55976-6
ISBN:	9783319559766$q(electronic bk.)

Newton's methodan updated approach of Kantorovich's theory /
Ezquerro Fernandez, Jose Antonio.

Newton's methodan updated approach of Kantorovich's theory /[electronic resource] :by Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron. - Cham :Springer International Publishing :2017. - xii, 166 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8046. - Frontiers in mathematics..

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.

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.

ISBN: 9783319559766$q(electronic bk.)

Standard No.: 10.1007/978-3-319-55976-6doiSubjects--Topical Terms:

229208
Newton-Raphson method.

LC Class. No.: QA297.8

Dewey Class. No.: 518.26

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520 $a 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.
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