A geometric Newton method for Oja's vector field.
Newton's method for solving the matrix equation F(X) identical to 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.
Absil
P A
PA
Department of Mathematical Engineering, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium. absil@inma.ucl.ac.be
Ishteva
M
M
De Lathauwer
L
L
Van Huffel
S
S
D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D006801:Humans; D012815:Signal Processing, Computer-Assisted