Numerical Algorithms on the Affine Grassmannian
Lek‐Heng Lim, Ken Sze-Wai Wong, Ke Ye · SIAM Journal on Matrix Analysis and Applications · 2019
The affine Grassmannian is a noncompact smooth manifold that parameterizes all affine subspaces of a fixed dimension. It is a natural generalization of Euclidean space, points being zero-dimensional affine subspaces. We will realize the affine Grassmannian as a matrix manifold and extend Riemannian optimization algorithms including steepest descent, Newton method, and conjugate gradient, to real-valued functions on the affine Grassmannian. Like their counterparts for the Grassmannian, they rely only on standard numerical linear algebra and are readily computable.