In this paper, we first propose a novel generalized power iteration (GPI) method to solve the quadratic problem on the Stiefel manifold (QPSM) as $$min_{W^{T}W=I}$$ m i n W T W = I Tr(W T AW − 2W T B) along with the theoretical analysis. Accordingly, its special case known as the orthogonal least square regression (OLSR) is under further investigation… (More)