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Random Matrices in Numerical Linear Algebra

Friday, March 25, 3PM – 5PM
ACES 6.304

Ioana Dumitriu, Washington University

The relationship between random matrix theory and numerical linear algebra now spans more than three decades, and it is ever growing and expanding. From analyzing the condition number of a "typical" matrix (Demmel '88, Edelman '89), to understanding why certain exponential worst-case algorithms behave very well in practice (Spielman-Teng'01), and from approximating low-rank matrices (Liberty-Woolfe-Martinsson-Rokhlin-Tygert '07, Halko-Martinsson-Tropp '09) to building communication-avoiding algorithms for eigenvalue computations (Ballard-Demmel-Dumitriu '10), random matrix results (along with actual random matrices) have been used to understand, speed up, and even stabilize numerical linear algebra algorithms. We will survey some of the work mentioned above, and present some recent contributions as well as avenues for future work.

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