English

A geometric Newton method for Oja's vector field

Numerical Analysis 2010-03-11 v1

Abstract

Newton's method for solving the matrix equation F(X)AXXXTAX=0F(X)\equiv AX-XX^TAX=0 runs up against the fact that its zeros are not isolated. This is due to a symmetry of FF by the action of the orthogonal group. We show how differential-geometric techniques can be exploited to remove this symmetry and obtain a ``geometric'' Newton algorithm that finds the zeros of FF. The geometric Newton method does not suffer from the degeneracy issue that stands in the way of the original Newton method.

Keywords

Cite

@article{arxiv.0804.0989,
  title  = {A geometric Newton method for Oja's vector field},
  author = {P. -A. Absil and M. Ishteva and L. De Lathauwer and S. Van Huffel},
  journal= {arXiv preprint arXiv:0804.0989},
  year   = {2010}
}
R2 v1 2026-06-21T10:28:17.076Z