Rice University

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Lecture/Lecture Series

Computational and Applied Mathematics

Speaker: Florian Potra
Department of Mathematics and Statistics
University of Maryland, Baltimore County

A superquadratic variant of Newton's method

Thursday, March 23, 2017
4:00 PM  to 5:00 PM

1049  Duncan Hall
Rice University
6100 Main St
Houston, Texas, USA

We present the first Q-superquadratically convergent version of Newton's method for solving operator equations in Banach spaces that requires only one operator value and one inverse of the Fr\'{e}chet derivative per iteration. The R-order of convergence is at least 2.4142. A semi-local analysis provides sufficient conditions for existence of a solution and convergence. The local analysis assumes that a solution exists and shows that the method converges from any starting point belonging to an explicitly defined neighbourhood of the solution called the ball of attraction.



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