2008 • Journal Article
A Geometric Newton Method for Oja's Vector Field.
Authors:
Absil, Pierre-Antoine ,
Ishteva, Mariya,
De Lathauwer, Lieven,
Van Huffel, Sabine
Published in:
Neural computation
Volume: 21 • Number: 5 • Pages: 1415-33
Newton's method for solving the matrix equation F(X) identical with AX - XX(T)AX = 0 runs up against the fact that its zeros are not isolated. This is due to a symmetry of F 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 F. The geometric Newton method does not suffer from the degeneracy issue that stands in the way of the original Newton method.