Joint Colloquium: Alex Townsend -- Continuous analogues of matrix factorizations

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 thecontinuous 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.