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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.

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