Finding structure with randomness
Friday, April 16, 2021
11AM – 12PM
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 the randomized singular value decomposition (SVD) algorithm, perhaps the most widely used method that has emerged from this research program. The randomized SVD algorithm supports 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.
Joel A. Tropp is Steele Family Professor of Applied and Computational Mathematics at Caltech. His research centers on data science, applied mathematics, numerical algorithms, and random matrix theory. He attained the Ph.D. degree in Computational Applied Mathematics at the University of Texas at Austin in 2004, and he joined Caltech in 2007. 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.
(The Babuška Forum series was started by Professor Ivo Babuška several years ago to expose students to interesting and curious topics relevant to computational engineering and science with technical content at the graduate student level (i.e. the focus of the lectures is on main ideas with some technical content). Seminar credit is given to those students who attend.)