This is not the latest version of this item. The latest version can be found here.
Accelerated Residual Methods for the Iterative Solution of Systems of Equations
Name
17m1141369.pdf
Size
1.75 MB
Format
Adobe PDF
Checksum (MD5)
cf64b4e8747d1fd7f58031f3f2139a01
Author(s)
Nguyen, N. C.
Fernandez, P.
Freund, R. M.
Peraire, J.
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.
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.
Persistent DSpace Link
DOI of Published Version
http://dx.doi.org/10.1137/17M1141369
