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2008

A geometric Newton method for Oja's vector field

Absil, P. -A., Ishteva, M., De Lathauwer, L. et al.

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Newton's method for solving the matrix equation $F(X)\equiv AX-XX^TAX=0$ 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.

A geometric Newton method for Oja's vector field · Around

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F. R. Gantmacher,
1959
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Shoshichi Kobayashi and Katsumi Nomizu,
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1994
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Wei-Yong Yan, Uwe Helmke, and John B. Moore,
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S. Eisenstat and H. Walker,
1996
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P.-A. Absil, R. Mahony, and R. Sepulchre,

2004

Cited alongside, same era.

P.-A. Absil, R. Sepulchre, and R. Mahony,

2008

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