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Numerical Algorithms on the Affine Grassmannian
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wong, Ken S. |
| Copyright Year | 2018 |
| 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://galton.uchicago.edu/~lekheng/work/affine.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Algorithm Arabic numeral 0 Computable function Conjugate gradient method Generalization (Psychology) Gradient descent Immunostimulating conjugate (antigen) Mathematical optimization Newton's method Numerical analysis Numerical linear algebra manifold |
| Content Type | Text |
| Resource Type | Article |
