**Sparse matrices, sparse signals,**

**and sparse algorithms**

**Anna Gilbert**

**Mathematics Department**

**University of Michigan**

**Abstract:** The past 10 years have seen a confluence of research in sparse approximation amongst computer science, mathematics, and electrical engineering. Sparse approximation encompasses a large number of mathematical, algorithmic, and signal processing problems which all attempt to balance the size of a (linear) representation of data and the fidelity of that representation. I will discuss several of the basic algorithmic problems and their solutions, focusing on special classes of matrices. I will conclude with an application in biological testing.

**Bio: **Anna Gilbert has an S.B. degree from the University of Chicago and a Ph.D. from Princeton University, both in mathematics. In 1997, she was a postdoctoral fellow at Yale University and AT&T Labs-Research. From 1998 to 2004, she was a member of technical staff at AT&T Labs-Research in Florham Park, NJ. Her research interests include analysis, probability, networking, and algorithms. She is especially interested in randomized algorithms with applications to harmonic analysis, signal and image processing, networking, and massive datasets.

**Tuesday, April 14**

**EECS Room 1005**

**4:00-5:00 pm**