On Hessian limit directions along non-oscillating gradient trajectories
Classical Analysis and ODEs
2013-11-14 v1 Algebraic Geometry
Abstract
Given a non-oscillating gradient trajectory G of a real analytic function f, we show that the limit v of the secants at the limit point O of G along the trajectory G is an eigen-vector of the limit of the direction of the Hessian matrix Hess (f) at O along G. The same holds true at infinity if the function is globally subanalytic. We also deduce some interesting estimates along the trajectory.
Keywords
Cite
@article{arxiv.1103.0729,
title = {On Hessian limit directions along non-oscillating gradient trajectories},
author = {Vincent Grandjean},
journal= {arXiv preprint arXiv:1103.0729},
year = {2013}
}