## IMA Postdoc Seminar (November 17, 2009)

**Speaker:** Maki, Kara (IMA)

**Title: **Experimental determination of the likelihood of catastrophic instability in Gaussian elimination.

**Abstract: **The growth factor of a matrix quantifies the amount of potential error growth
when a linear system is solved by Gaussian elimination with partial pivoting. While the growth factor has a maximum of
$2^{n-1}$ for an $n \times n$ matrix, experience
suggests the occurrence of matrices with exponentially large growth factors is
extremely rare. To add computational evidence, we implemented a multicanonical Monte Carlo
method to explore the tails of growth factor probability distributions for random matrices. .