Past Event: Oden Institute Seminar

Optimal Preconditioning?

Alperen Ergur, Assistant Professor, Department of Mathematics and Computer Science, UTSA

Abstract

Preconditioning is the art of finding computationally light transformations of problem data that improves run time and accuracy of numerical algorithms. Optimal diagonal preconditioners have been studied in numerical linear algebra since the 60's and have been subject to a flurry of papers in the last few years. We consider the optimal preconditioning problem in a much general framework:  (1) We are interested in linear and non-linear algebra problems,  (2) We are interested in using block-diagonal matrices and other matrix groups for preconditioning.   We'll explain how this generality still allows a convex optimization formulation when we use explicit geodesic paths on matrix groups. We'll then proceed to analysis of geodesically convex optimization algorithms, followed by some experiments for preconditioning with block-diagonal matrices.  Time permits, applications of this framework on accelerating non-linear algebra algorithms will be explained as well.    The talk does not assume any background on Lie theory, algebraic geometry, preconditioning, or convex optimization: we'll introduce the concepts,  and we hope to learn from the audience as much the audience learns from the talk.    Joint work with Levent Dogan of Ruhr-Universitat-Bochum and Elias Tsigaridas of INRIA, Paris.

Biography

Alperen Ergur is an Assistant Professor in the Departments of Mathematics and Computer Science at UTSA. Prior to joining UTSA, he held positions as a postdoctoral researcher with the Algorithms Group at Carnegie Mellon University and as an Einstein Postdoctoral Fellow in the Discrete Mathematics Department at TU Berlin. He also had the opportunity to collaborate briefly with Cynthia Vinzant.  His research interests are in real algebraic geometry, discrete and convex geometry, high dimensional probability, randomized numerical algorithms, optimization, and lately reinforcement learning.