082 Heather Wilber

Heather Wilber (Oden Institute, University of Texas at Austin)// Low rank numerical methods via rational function approximation // Abstract: In this talk, we apply classical ideas in approximation theory to design low rank numerical methods for a range of applications in scientific computing, including the solving of certain linear systems, matrix equations, and partial differential equations. The primary workhorse in our approach and analysis is the alternating direction implicit (ADI) method, and we explore how this special splitting algorithm is linked to a wealth of concepts from applied mathematics, including Laplace’s equation and conformal maps for doubly-connected regions, matrix and operator function evaluation, digital filter design, and the low rank properties of matrices with special displacement structures.