cauchy's method
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2021 ◽  
pp. 107558
Author(s):  
Jean-Paul Brasselet ◽  
Nguyn̂̃n Thị Bích Thủy

Author(s):  
Nicole Vorderobermeier

We prove the analyticity of smooth critical points for O’Hara’s knot energies [Formula: see text], with [Formula: see text] and [Formula: see text], subject to a fixed length constraint. This implies, together with the already established regularity results for O’Hara’s knot energies, that bounded energy critical points of [Formula: see text] subject to a fixed length constraint are not only [Formula: see text] but also analytic. Our approach is based on Cauchy’s method of majorants and a decomposition of the gradient that was adapted from the Möbius energy case [Formula: see text].


2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Mohamed Lamine Sahari

Let p be a complex polynomial of fixed degree n. In this paper we show that Cauchy’s method may fail to find all zeros of p for any initial guess z0 lying in the complex plane and we propose several ways to find all zeros of a given polynomial using scaled Cauchy’s methods.


2008 ◽  
Vol 339 (2) ◽  
pp. 954-969 ◽  
Author(s):  
J.A. Ezquerro ◽  
M.A. Hernández ◽  
N. Romero

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