Rodolphe Sepulchre, June 2013
Rodolphe Sepulchre will visit Caltech on 3 June 2013 (Mon).
|9:30a||Richard Murray, 109 Steele Lab|
|9:45a||Meet with Richard's NCS group, 110 Steele
|11:45a||Lunch with Venkat, CMS faculty|
|1:30p||Seminar, 121 ANB|
|3:00p||Venkat Chandrasekaran, 300 ANB|
|3:45p||Lijun Chen, 202 ANB|
|4:30p||(free), 320 ANB|
The geometry of (thin) SVD revisited for large-scale computations
University of Liege, Belgium
The talk will introduce a riemannian framework for large-scale computations over the set of low-rank matrices. The foundation is geometric and the motivation is algorithmic, with a bias towards efficient computations in large-scale problems. We will explore how classical matrix factorizations connect the riemannian geometry of the set of fixed-rank matrices to two well-studied manifolds: the Grassmann manifold of linear subspaces and the cone of positive definite matrices. The theory will be illustrated on various applications, including low-rank Kalman filtering, linear regression with low-rank priors, matrix completion, and the choice of a suitable metric for Diffusion Tensor Imaging.