Compressed Modes and Localized Density Matrices

Start: 04/27/2015 - 12:00pm
End  : 04/27/2015 - 1:00pm

Applied Math Seminar

Rongjie Lai (Rensselaer Polytechnic Institute)


 $\ell_1$ regularization for sparsity has played important role in recent developments in many fields including signal processing, statistics, optimization. The concept of sparsity is usually for the coefficients (i.e., only a small set of coefficients are nonzero) in a well-chosen set of modes (e.g. a basis or dictionary) for representation of the corresponding vectors or functions. Our recent work investigate a new use of sparsity-promoting techniques to produce ‚Äúcompressed modes" - modes that are sparse and localized in space - for efficient solutions of constrained variational problems in mathematics and physics.  I first will discuss L1 regularized variational Schrodinger equations for creating spatially localized modes and orthonormal basis, which can efficiently represent localized functions.  In addition, I will also discuss our recent work on localized density matrices and their linear scaling algorithms.


Kravis 100