We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness our method, we perform numerical experiments that number iterations scales square root condition number, and also compare existing state-of-the-art quasi-Newton methods on Stiefel manifold. Our show outperforms some large, ill-c...

Chromatic orthogonality is defined as the possibility of independently addressing different photosensitive sites using light beams colors. After its initial study in synthetic chemistry, this property has been applied many other fields, such lithography, chemical biology and catalysis. This short account gives an overview some significant work field last two decades.

we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).