LEADER 03629nam 22005895 450 001 9910254278503321 005 20220407001018.0 010 $a3-319-55976-1 024 7 $a10.1007/978-3-319-55976-6 035 $a(CKB)4340000000062040 035 $a(MiAaPQ)EBC4901920 035 $a(DE-He213)978-3-319-55976-6 035 $a(PPN)203668960 035 $a(EXLCZ)994340000000062040 100 $a20170706d2017 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aNewton?s method: an updated approach of Kantorovich?s theory /$fby José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (166 pages) 225 1 $aFrontiers in Mathematics,$x1660-8046 311 $a3-319-55975-3 320 $aIncludes bibliographical references. 327 $aThe 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. 330 $aThis book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular. 410 0$aFrontiers in Mathematics,$x1660-8046 606 $aOperator theory 606 $aComputer mathematics 606 $aIntegral equations 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090 615 0$aOperator theory. 615 0$aComputer mathematics. 615 0$aIntegral equations. 615 14$aOperator Theory. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aIntegral Equations. 676 $a511.4 700 $aEzquerro Fernández$b José Antonio$4aut$4http://id.loc.gov/vocabulary/relators/aut$0913709 702 $aHernández Verón$b Miguel Ángel$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254278503321 996 $aNewton?s Method: an Updated Approach of Kantorovich?s Theory$92047107 997 $aUNINA