國立虎尾科技大學 |

Newton's method = an updated approach of Kantorovich's theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Newton's method/ by 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

Newton's method = an 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

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

528526
Newton-Raphson method.

LC Class. No.: QA297.8

Dewey Class. No.: 518.26

Newton's method = an updated approach of Kantorovich's theory /
LDR:02436nam a2200325 a 4500 001 923086
003 DE-He213
005 20170706120450.0
006 m d
007 cr nn 008maaau
008 190625s2017 gw s 0 eng d
020 $a 9783319559766 $q (electronic bk.)
020 $a 9783319559759 $q (paper)
024 7 $a 10.1007/978-3-319-55976-6 $2 doi
035 $a 978-3-319-55976-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA297.8
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
082 0 4 $a 518.26 $2 23
090 $a QA297.8 $b .E99 2017
100 1 $a Ezquerro Fernandez, Jose Antonio. $3 1199141
245 1 0 $a Newton's method $h [electronic resource] : $b an updated approach of Kantorovich's theory / $c by Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron.
260 $a Cham : $c 2017. $b Springer International Publishing : $b Imprint: Birkhauser,
300 $a xii, 166 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in mathematics, $x 1660-8046
505 0 $a 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.
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.
650 0 $a Newton-Raphson method. $3 528526
650 0 $a Iterative methods (Mathematics) $3 528050
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Operator Theory. $3 672127
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 669338
650 2 4 $a Integral Equations. $3 672359
700 1 $a Hernandez Veron, Miguel Angel. $3 1199142
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Frontiers in mathematics. $3 888364
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-55976-6
950 $a Mathematics and Statistics (Springer-11649)