Dr. Eric Weber, 'A Randomized Distributed Linear Solver', TADS Lunch-n-Learn

Presenter: Dr. Eric Weber

Title: A Randomized Distributed Linear Solver

Abstract: We consider the problem of solving a system of linear equations when the equations are distributed across multiple nodes of a network.  We present an algorithm based on the Kaczmarz method to find solutions, or generalized solutions, to the system of equations.  We present convergence guarantees for both consistent and inconsistent systems, and demonstrate that the algorithm can be used to approximate the least-squares solution.  We also introduce a randomized variant that allows for a more refined convergence analysis of the method based on the spectral data of the coefficient matrix.

Bio: Dr. Eric Weber holds a Ph.D. in Mathematics from the University of Colorado.  His research interests include harmonic analysis, approximation theory and data science.  Past research includes developing novel wavelet transforms for image processing, and reproducing kernel methods for the harmonic analysis of fractals.  Current research projects include the development of new algorithms for processing distributed spatiotemporal datasets in order to increase understanding of human dynamics; extending alternating projection methods for optimization in non-Euclidean geometries; using harmonic analysis techniques for understanding the approximation properties of neural networks; and developing machine learning techniques to improve the diagnosis of severe wind occurrences.

After the presentation, there will be a short time for discussion and questions afterwards.  Please feel free to bring your lunch!