A Distributed Linear Solver via the Kaczmarz Algorithm

Eric Weber (Iowa State University)

Abstract: The Kaczmarz algorithm is a method for solving linear systems of equations that was introduced in 1937.  The algorithm is a powerful tool with many applications in signal processing and data science that has enjoyed a resurgence of interest in recent years.  We'll discuss some of the history of the Kaczmarz algorithm as well as describe some of the recent interest and applications.  We'll then discuss how the algorithm can be used as a consensus method to process data in a distributed environment.

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; 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.