Speaker: Florian Potra, UMBC
Title:
A superquadratic variant of Newton's method
Abstract: 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.
Time: Friday, October 6, 2017, 3:30-4:20 p.m.
Department of Mathematical Sciences
George Mason University
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