Randomized methods for low-rank approximation

Among the most exciting recent developments in numerical linear algebra is the advent of randomized algorithms that are fast, scalable, robust, and reliable. Low-rank approximation is among the most important problems for which randomization has had a significant impact. In this talk I will try to summarize the most successful randomized algorithms for low-rank approximation, comparing their efficiency and approximation performance, and discuss subtle issues including stability, practical efficiency, and the treatment of structured cases, e.g. symmetric (positive semidefinite). Time and progress permitting, I will discuss low-rank approximation for tensor problems.

Yuji Nakatsukasa is an associate professor at Oxford University Mathematical Institute, and a fellow (official student) of Christ Church. His research focus is numerical analysis, with emphasis on eigenvalue problems in numerical linear algebra and rational approximation theory. Prior to his current affiliation, he had positions at National Institute of Informatics, Oxford, Tokyo, and Manchester. He obtained his PhD in Applied Mathematics from UC Davis in 2011.

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