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## Computational Colloquium Series

Speaker: Dr. Alex Townsend, Department of Mathematics, MIT Place : ILC 302 Date/Time: Thursday, Feb. 4, 3:00-4:00pm Title: Continuous analogues of matrix factorizations Abstract: A fundamental idea in matrix linear algebra is the factorization of a matrix into simpler matrices, such as orthogonal, tridiagonal, and triangular. In this talk we extend this idea to a continuous setting, asking: "What are the continuous analogues of matrix factorizations?" The answer we develop involves functions of two variables, an iterative variant of Gaussian elimination, and sufficient conditions for convergence. This leads to a test for non-negative definite kernels, a continuous definition of a triangular quasimatrix (a matrix whose columns are functions), and a fresh perspective on a classic subject. This is work is with Nick Trefethen. http://math.mit.edu/~ajt/

Last modified: Sun Jan 31 21:12:28 MST 2016