Abstract
We consider Anderson extrapolation to accelerate the (stationary) Richardson iterative method for sparse linear systems. Using an Anderson mixing at periodic intervals, we assess how this benefits convergence to a prescribed accuracy. The method, named alternating Anderson–Richardson, has appealing properties for high-performance computing, such as the potential to reduce communication and storage in comparison to more conventional linear solvers. We establish sufficient conditions for convergence, and we evaluate the performance of this technique in combination with various preconditioners through numerical examples. Furthermore, we propose an augmented version of this technique.
| Original language | English |
|---|---|
| Article number | e2241 |
| Journal | Numerical Linear Algebra with Applications |
| Volume | 26 |
| Issue number | 4 |
| DOIs | |
| State | Published - Aug 2019 |
Funding
Alternating Anderson-Richardson This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE)." The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/ downloads/doe-public-access-plan). I would like to thank Michele Benzi (Emory University) and Phanish Suryanarayana (Georgia Institute of Technology) for the helpful suggestions and Steven Hamilton (Oak Ridge National Laboratory) for providing some of the test matrices used. This work was supported in part by the United States Department of Energy (Office of Science) under Grant ERKJ247. This research used resources of the Oak Ridge Leadership Computing Facility, which is a Department of Energy Office of Science User Facility supported under Contract DE-AC05-00OR22725. I would like to thank Michele Benzi (Emory University) and Phanish Suryanarayana (Georgia Institute of Technology) for the helpful suggestions and Steven Hamilton (Oak Ridge National Laboratory) for providing some of the test matrices used. This work was supported in part by the United States Department of Energy (Office of Science) under Grant?ERKJ247. This research used resources of the Oak Ridge Leadership Computing Facility, which is a Department of Energy Office of Science User Facility supported under Contract DE-AC05-00OR22725. There are no conflicts of interest to this work.
| Funders | Funder number |
|---|---|
| Department of Energy Office of Science | |
| US Department of Energy | |
| United States Department of Energy | |
| U.S. Department of Energy | DE-AC05-00OR22725 |
| Office of Science | Grant?ERKJ247, ERKJ247 |
| Georgia Institute of Technology |
Keywords
- Anderson acceleration
- Richardson iteration
- fixed-point scheme
- projection method