Wolfgang Quapp

Mathematisches Institut, Universit"at Leipzig, PF 100920, D-04009 Leipzig, Germany

Comment on "Exploring the potential energy landscape of the Thomson problem
 via Newton homotopies" [J. Chem. Phys. 142, 194113 (2015)]

abstract:

We report that the Newton homotopy used in the paper 
[D. Mehta et al. J. Chem. Phys. 142, 194113 (2015)] 
is equivalent to the method of Newton trajectories.
We use this method to clear the picture of the   
Griewank and Osborne function used as an example in the paper 
by Mehta et al..  
They describe the state of affairs of numerical experiments, while
we can derive an explicit formula for the Newton trajectories of this
function.
With such a formula we can explain the findings of the commented paper.


submitted to J. Chem. Phys.