Newton-type Methods on Stiefel Manifolds

Jochen Trumpf and Knut Hüper

In this talk we will discuss to what extent the classical Rayleigh Quotient Iteration (RQI) can be interpreted as a Newton iteration, and to what extent it cannot. We will present at least three notions of Newton iteration and explain their subtle and not so subtle differences. Our framework will then be applied to the natural generalisation of RQI to Stiefel manifolds. We comment on local convergence analysis and relate our results to those by Shub, and to more recent ones by Absil et al., Dedieu et al., Edelman et al., and Manton.