**Time: ** Tuesday, May 1, 2018, 2:00pm @ MTH3206

**Speaker: ** Weilin Li (UMD)

**Title: ** Subspace methods and smallest singular value of Vandermonde matrices

**Abstract: ** This talk consists of two parts. The first part examines the following problem: Given a finite subset X of the one-dimensional torus and of cardinality S, and given an integer M >= S, estimate the smallest singular value of the MxS Vandermonde matrix associated with X and M. We show how to obtain accurate lower bounds using duality and Fourier analysis. The second part connects this problem to topics in signal processing such as super-resolution and parameter estimation. The smallest singular value of such Vandermonde matrices essentially characterize the stability of a collection of algorithms, called subspace methods, to noise. This is joint work with Wenjing Liao.

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