Abstract
The preconditioned Barzilai-Borwein method is derived and applied to the numerical solution of large, sparse, symmetric and positive definite linear systems that arise in the discretization of partial differential equations. A set of well-known preconditioning techniques are combined with this new method to take advantage of the special features of the Barzilai-Borwein method. Numerical results on some elliptic test problems are presented. These results indicate that the preconditioned Barzilai-Borwein method is competitive and sometimes preferable to the preconditioned conjugate gradient method.
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Communicated by C. Brezinski
This author was partially supported by the Parallel and Distributed Computing Center at UCV.
This author was partially supported by BID-CONICIT, project M-51940.
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Molina, B., Raydan, M. Preconditioned Barzilai-Borwein method for the numerical solution of partial differential equations. Numer Algor 13, 45–60 (1996). https://doi.org/10.1007/BF02143126
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DOI: https://doi.org/10.1007/BF02143126
Keywords
- Barzilai-Borwein method
- conjugate gradient method
- incomplete Cholesky
- symmetric successive overrelaxation
- elliptic equations