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Advances in Complex Function Theory (Lecture Notes in Mathematics) by W. E. Kirwan (Repost)
Matrix Mathematics - Theory, Facts, and Formulas, Second Edition
Mathematics Probability, Markov Chains, Queues, and Simulation - The Mathematical Basis of Performance Modeling
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Mathematics LMSST - 24 Lectures on Elliptic Curves (London Mathematical Society Student Texts) by J. W. S. Cassels
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Mathematics Points fixes, z¨¦ros et la m¨¦thode de Newton
Posted on 2010-04-12
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More Jean-Pierre Dedieu ¡°Points fixes, z¨¦ros et la m¨¦thode de Newton" Cet ouvrage est consacr¨¦ aux points fixes d'applications diff¨¦rentiables, aux z¨¦ros de syst¨¨mes non-lin¨¦aires et ¨¤ la m¨¦thode de Newton. Il s'adresse ¨¤ des ¨¦tudiants de mast¨¨re ou pr¨¦parant l'agr¨¦gation de math¨¦matique et ¨¤ des chercheurs confirm¨¦s. La premi¨¨re partie est consacr¨¦e ¨¤ la m¨¦thode des approximations successives et confronte un point de vue ?syst¨¨mes dynamiques? (th¨¦or¨¨mes de Grobman-Hartman, de la vari¨¦t¨¦ stable) ¨¤ des exemples issus de l'analyse num¨¦rique. La seconde partie de cet ouvrage expose la m¨¦thode de Newton et ses d¨¦veloppements les plus r¨¦cents (th¨¦orie alpha de Smale, syst¨¨mes sous ou sur-d¨¦termin¨¦s). Elle pr¨¦sente une nouvelle approche de ce sujet et un ensemble de r¨¦sultats originaux publi¨¦s pour la premi¨¨re fois dans un ouvrage de langue fran?aise. This is an advanced text on fixed points, zeros of nonlinear systems and the Newton method. Its first part, devoted to fixed points, includes the Grobman-Hartman and the stable manifold theorems. The second part describes the Newton method from a modern point of view: Smale's alpha theory, underdetermined and overdetermined systems of equations. These results are illustrated by various examples from numerical analysis. "
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