A geometric Newton method for Oja’s vector field.

P.a. Absil, Mariya Ishteva, Lieven De Lathauwer, Sabine Van Huffel

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1415-1433
Number of pages19
JournalNeural Computation
Publication statusPublished - 1 May 2009


  • Mathematics
  • Numerical Analysis


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