Newton's method on Graßmann manifolds

Details Newton's method on Graßmann manifolds Newton's method on Graßmann manifolds

2007-09-14

arxiv.org/abs/0709.2205v2

Mathematics

Optimization and Control

36 pages, typos corrected and references added

Scientific paper

A general class of Newton algorithms on Gra{\ss}mann and Lagrange-Gra{\ss}mann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local quadratic convergence of the algorithm is shown under a suitable condition on the choice of coordinate systems. Our result extends and unifies previous convergence results for Newton's method on a manifold. Using special choices of the coordinates, new numerical algorithms are derived for principal component analysis and invariant subspace computations with improved computational complexity properties.

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