LEADER 04399nam 22006735 450 001 996418258603316 005 20200703184950.0 010 $a3-030-48702-4 024 7 $a10.1007/978-3-030-48702-7 035 $a(CKB)4100000011325715 035 $a(DE-He213)978-3-030-48702-7 035 $a(MiAaPQ)EBC6270572 035 $a(PPN)257359109 035 $a(EXLCZ)994100000011325715 100 $a20200703d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMild Differentiability Conditions for Newton's Method in Banach Spaces$b[electronic resource] /$fby José Antonio Ezquerro Fernandez, Miguel Ángel Hernández Verón 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (XIII, 178 p. 51 illus., 45 illus. in color.) 225 1 $aFrontiers in Mathematics,$x1660-8046 311 $a3-030-48701-6 327 $aPreface -- The Newton-Kantorovich theorem -- Operators with Lipschitz continuous first derivative -- Operators with Hölder continuous first derivative -- Operators with Hölder-type continuous first derivative -- Operators with w-Lipschitz continuous first derivative -- Improving the domain of starting points based on center conditions for the first derivative -- Operators with center w-Lipschitz continuous first derivative -- Using center w-Lipschitz conditions for the first derivative at auxiliary points. 330 $aIn this book the authors use a technique based on recurrence relations to study the convergence of the Newton method under mild differentiability conditions on the first derivative of the operator involved. The authors? technique relies on the construction of a scalar sequence, not majorizing, that satisfies a system of recurrence relations, and guarantees the convergence of the method. The application is user-friendly and has certain advantages over Kantorovich?s majorant principle. First, it allows generalizations to be made of the results obtained under conditions of Newton-Kantorovich type and, second, it improves the results obtained through majorizing sequences. In addition, the authors extend the application of Newton?s method in Banach spaces from the modification of the domain of starting points. As a result, the scope of Kantorovich?s theory for Newton?s method is substantially broadened. Moreover, this technique can be applied to any iterative method. This book is chiefly intended for researchers and (postgraduate) students working on nonlinear equations, as well as scientists in general with an interest in numerical analysis. 410 0$aFrontiers in Mathematics,$x1660-8046 606 $aOperator theory 606 $aNumerical analysis 606 $aIntegral equations 606 $aDifferential equations 606 $aPartial differential equations 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aOperator theory. 615 0$aNumerical analysis. 615 0$aIntegral equations. 615 0$aDifferential equations. 615 0$aPartial differential equations. 615 14$aOperator Theory. 615 24$aNumerical Analysis. 615 24$aIntegral Equations. 615 24$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 676 $a515.732 700 $aEzquerro Fernandez$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 $a996418258603316 996 $aMild Differentiability Conditions for Newton's Method in Banach Spaces$92359370 997 $aUNISA