# Numerical Analysis and Scientific Computing Seminar

## How Long Does it Take to Compute the Eigenvalues of a Random Symmetric Matrix?

**Speaker:**
Christian Pfrang, Brown University

**Location:**
Warren Weaver Hall 1302

**Date:**
March 9, 2012, 10 a.m.

**Synopsis:**

We present the results of an empirical study of the performance of the QR and Toda eigenvalue algorithms on random symmetric matrices and observe a form of universality for the deflation time statistics for random matrices within the Wigner class. We also provide a quantitative statistical picture of the known fact that the shifted QR algorithm typically deflates at the lower-right corner of the matrix and present how certain divide and conquer algorithms for eigenvalue problems are related to the Hamiltonian point of view.