BCAM Seminar - Newton-Kantorovich Theory and some of its variations
Date: Fri, Jun 26 2009
Location: Universidad de la Rioja, Spain
Speakers: José Manuel GUTIERREZ
Newton-Kantorovich Theory and some of its variations
In 1948 the Soviet mathematician L. V. Kantorovich proposed the extension of Newton's method for solving nonlinear equations to functional spaces. Perhaps the most relevant aspect of Kantorovich's result is the combination of techniques in Numerical Analysis and Functional Analysis. Another peculiarity of Kantorovich's theorem is that it does not assume the existence of a solution. So this theorem can be seen as an existence and uniqueness result and not only as a convergence theorem for a given method. Kantorovich's theory can be applied to a wide range of nonlinear problems, such as integral equations, ordinary and partial differential equations, variational problems, etc.
There exist numerous versions of Kantorovich's theorem, which differ both in assumptions and results. In this talk we present some of these variations, making especial emphasis on the ones achieved by the speaker and by his research group.
In 1948 the Soviet mathematician L. V. Kantorovich proposed the extension of Newton's method for solving nonlinear equations to functional spaces. Perhaps the most relevant aspect of Kantorovich's result is the combination of techniques in Numerical Analysis and Functional Analysis. Another peculiarity of Kantorovich's theorem is that it does not assume the existence of a solution. So this theorem can be seen as an existence and uniqueness result and not only as a convergence theorem for a given method. Kantorovich's theory can be applied to a wide range of nonlinear problems, such as integral equations, ordinary and partial differential equations, variational problems, etc.
There exist numerous versions of Kantorovich's theorem, which differ both in assumptions and results. In this talk we present some of these variations, making especial emphasis on the ones achieved by the speaker and by his research group.
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