A new adaptive GMRES algorithm for achieving high accuracy [electronic resource].
- Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 1996.
- Physical Description:
- pages 7, Paper 67 : digital, PDF file
- Additional Creators:
- United States. Department of Energy. Office of Scientific and Technical Information
- Restrictions on Access:
- Free-to-read Unrestricted online access
- GMRES(k) is widely used for solving nonsymmetric linear systems. However, it is inadequate either when it converges only for k close to the problem size or when numerical error in the modified Gram-Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES (k) which tunes the restart value k based on criteria estimating the GMRES convergence rate for the given problem is proposed here. The essence of the adaptive GMRES strategy is to adapt the parameter k to the problem, similar in spirit to how a variable order ODE algorithm tunes the order k. With FORTRAN 90, which provides pointers and dynamic memory management, dealing with the variable storage requirements implied by varying k is not too difficult. The parameter k can be both increased and decreased-an increase-only strategy is described next followed by pseudocode.
- Published through SciTech Connect., 12/31/1996., "conf-9604167--vol.1", "DE96015306", ": Grant F49620-92-J-0236", Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 9-13 Apr 1996., Watson, L.T.; Walker, H.F.; Kapania, R.K.; Sosonkina, M., and Front Range Scientific Computations, Inc., Lakewood, CO (United States)
- Funding Information:
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