Wednesday, November 19, 2014
12:00 - 1:00 pm (Lunch Provided)
Amos Eaton Room 402
Speaker: Rongjie Lai, Assistant Professor Mathematical Sciences, RPI
Title: "COMPRESSED MODES FOR VARIATIONAL PDEs"
Abstract: $/ell_1$ regularization for sparsity has played an important role in recent developments in many fields inculding 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. In this talk, I will discuss our recent work on a new use of sparsity-promoting techniques to produce "compressed modes" - modes that are sparse and localized in space - for efficient solutions of constrained variational problems in mathematics and physics. In this talk, I will discuss L1 regularized variational Schrodinger equations for creating spatially localized modes and orthonormal basis, which can efficiently represent localized functions and has promising potential to a variety of applications in many fields such a signal processing, numerical PDEs, computational physics etc. In addition, I will aslo discuss our recent work on compressed density function which can be viewed as a convex version of the compressed modes based in lifting idea.