This collaborative project aims to bridge the theoretical and practical aspects of designing efficient and robust solvers for linear systems with Laplacian matrices of graphs. Prof. Gilbert and his team plan to develop code packages that have good practical performance as well as provable guarantees in the worst case. 

The goal is a package that is able to solve Laplacian linear systems with a billion non-zeros in a few seconds on a workstation. Graph Laplacians in these size ranges occur frequently in image and signal processing and in network analytics, and in turn have applications in data mining, machine learning, operations research, circuit simulation, and biomedical imaging.