Events Calendar

CS Colloq. Prof. Van Vu

Talk title: The condition number of a random matrix Speaker:Prof. Van Vu from Rutgers University Host: Prof. Shang-Hua Teng Abstract: The condition number plays a crucial role in all computational problems involving a large matrix. The problem of determining the condition number of a random matrix (with independent entries) was first raised by von Neumann and Goldstine in the 1940s, in a series of papers which later has become the starting point of numerical analysis. von Neumann-Golstine problem was solved for the case when the entries of the matrix have gaussian distribution by Edelman in 1980s. Edelman computed the limiting distribution of the condition number, using special feature of gaussian matrices. This computation does not extend to any other model of random matrices (such as Bernoulli). On the other hand, it has been conjectured, for quite sometime, that the same distribution should hold in these cases as well. Recently, Tao and Vu proved this conjecture, and thus solved von Neumann-Goldstine problem in the general case. As a corollary, we proved a conjeture of Spielman and Teng about the distribution of the least singular value. I will present a sketch of the proof, which starts with random sampling techniques. Bio: TBA

Location: Seeley G. Mudd Building (SGM) - 601

Audiences: Everyone Is Invited

Contact: CS Front Desk