Accelerated Residual Methods for the Iterative Solution of Systems of Equations
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17m1141369.pdf
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1.75 MB
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Author(s)
Nguyen, N.C.
Fernandez, Pablo
Freund, R. M.
Peraire, Jaime
Date Issued
2018
Journal
SIAM Journal on Scientific Computing
Citation
Nguyen, N. C., P. Fernandez, R. M. Freund, and J. Peraire. “Accelerated Residual Methods for the Iterative Solution of Systems of Equations.” SIAM Journal on Scientific Computing 40, no. 5 (January 2018): A3157–A3179. doi:10.1137/17m1141369.
Version
Final published version
Abstract
© 2018 Society for Industrial and Applied Mathematics. We present accelerated residual methods for the iterative solution of systems of equations by leveraging recent developments in accelerated gradient methods for convex optimization. The stability properties of the proposed method are analyzed for linear systems of equations by using the finite difference equation theory. Next, we introduce a residual descent restarting strategy and an adaptive computation of the acceleration parameter to enhance the robustness and efficiency of our method. Furthermore, we incorporate preconditioning techniques into the proposed method to accelerate its convergence. We demonstrate the performance of our method on systems of equations resulting from the finite element approximation of linear and nonlinear partial differential equations. In a variety of test cases, the numerical results show that the proposed method is competitive with the pseudo-time-marching method, Nesterov's method, and Newton-Krylov methods. Finally, we discuss some open issues that should be addressed in future research.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Sloan School of Management
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/17M1141369
