Mathematics Colloquium

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Finding structure with randomness: Randomized SVD algorithms

Speaker: Joel A. Tropp, California Institute of Technology

Location: Online

Videoconference link: https://nyu.zoom.us/rec/share/W4Id9U7fxcTd3ywvDj_hXdPGhWdQw6p0nXIq11Bj7qum7Srj2ceR3dLlWKb6Vs2I.ppjWTFPTKCnhuZrv

Date: Monday, January 31, 2022, 3:45 p.m.

Synopsis:

Over the last 20 years, randomized algorithms have revolutionized the field of matrix computations. These new methods can efficiently and robustly solve huge linear algebra problems that were previously inaccessible.

This talk introduces randomized singular value decomposition (SVD) algorithms, perhaps the most widely used methods that have emerged from this research program. These algorithms support large-scale linear regression, principal component analysis, proper orthogonal decomposition, and many other methods for data reduction and summarization. The talk offers a high-level view of how randomness facilitates the SVD computation, the kinds of theoretical guarantees it allows, and some applications in science and engineering.

For more information, see the papers arXiv:0909.4061 and arXiv:2002.01387.

Bio: Joel A. Tropp is Steele Family Professor of Applied and Computational Mathematics at Caltech. He earned the Ph.D. degree in Computational Applied Mathematics from the University of Texas at Austin in 2004, and he joined Caltech in 2007. His research centers on mathematics of data, numerical algorithms, and random matrix theory. Prof. Tropp won the PECASE in 2008, and he was recognized as a Highly Cited Researcher in Computer Science each year from 2014–2018. He is co-founder and Section Editor of the SIAM Journal on Mathematics of Data Science (SIMODS), and he was co-chair of the inaugural 2020 SIAM Conference on the Mathematics of Data Science. Prof. Tropp was elected SIAM Fellow in 2019 and IEEE Fellow in 2020.