Abstract: This talk considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. We propose the eigenmatrix as a unified solution for these sparse recovery problems. The key is a data-driven construction with desired approximate eigenvalues and eigenvectors. We also discuss its multidimensional version and applications in free deconvolution.

About the speaker:  

Lexing Ying is a professor of mathematics at Stanford University. He received B.S. from Shanghai Jiaotong University in 1998 and Ph.D. from New York University in 2004. Before joining Stanford in 2012, he was a post-doc at Caltech and a professor at UT Austin. He received a Sloan Fellowship in 2007, an NSF Career Award in 2009, the Fengkang Prize in 2011, and the James H. Wilkinson Prize in 2013. He is an invited speaker of ICM 2022.