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S. Van Huffel
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Journal Articles
Publisher: Journals Gateway
Neural Computation (2009) 21 (5): 1415–1433.
Published: 01 May 2009
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Newton's method for solving the matrix equation 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.