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arXiv · 1607.01833

Numerical algorithms on the affine Grassmannian

Lek-Heng Lim·Ken Sze-Wai Wong·Ke Ye
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Abstract

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, these algorithms are in the style of Edelman--Arias--Smith --- they rely only on standard numerical linear algebra and are readily computable.

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Lek-Heng Lim, Ken Sze-Wai Wong, Ke Ye. 2016-07-06. Numerical algorithms on the affine Grassmannian. https://arxiv.org/abs/1607.01833

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