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024 7 $a10.1007/978-3-030-48702-7
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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 /$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 $aFrontiers in Mathematics,$x1660-8054
311 08$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   $aIn this book the authors use a technique based on recurrence relations to study the convergence of the Newton method under mild differentiability conditions on the first derivative of the operator involved. The authors? technique relies on the construction of a scalar sequence, not majorizing, that satisfies a system of recurrence relations, and guarantees the convergence of the method. The application is user-friendly and has certain advantages over Kantorovich?s majorant principle. First, it allows generalizations to be made of the results obtained under conditions of Newton-Kantorovich type and, second, it improves the results obtained through majorizing sequences. In addition, the authors extend the application of Newton?s method in Banach spaces from the modification of the domain of starting points. As a result, the scope of Kantorovich?s theory for Newton?s method is substantially broadened. Moreover, this technique can be applied to any iterative method. This book ischiefly intended for researchers and (postgraduate) students working on nonlinear equations, as well as scientists in general with an interest in numerical analysis.
410  0$aFrontiers in Mathematics,$x1660-8054
606   $aOperator theory
606   $aNumerical analysis
606   $aIntegral equations
606   $aDifferential equations
606   $aOperator Theory
606   $aNumerical Analysis
606   $aIntegral Equations
606   $aDifferential Equations
615  0$aOperator theory.
615  0$aNumerical analysis.
615  0$aIntegral equations.
615  0$aDifferential equations.
615 14$aOperator Theory.
615 24$aNumerical Analysis.
615 24$aIntegral Equations.
615 24$aDifferential Equations.
676   $a515.732
676   $a515.724
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   $a9910483979003321
996   $aMild Differentiability Conditions for Newton's Method in Banach Spaces$92359370
997   $aUNINA