A new adaptive GMRES algorithm for achieving high accuracy
- Virginia Polytechnic Inst., Blacksburg, VA (United States)
- Utah State Univ., Logan, UT (United States)
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.
- Research Organization:
- Front Range Scientific Computations, Inc., Lakewood, CO (United States)
- DOE Contract Number:
- FG05-88ER25068
- OSTI ID:
- 433394
- Report Number(s):
- CONF-9604167-Vol.1; ON: DE96015306; CNN: Grant F49620-92-J-0236; TRN: 97:000720-0069
- Resource Relation:
- Journal Volume: 5; Journal Issue: 4; Conference: Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 9-13 Apr 1996; Other Information: PBD: [1996]; Related Information: Is Part Of Copper Mountain conference on iterative methods: Proceedings: Volume 1; PB: 422 p.
- Country of Publication:
- United States
- Language:
- English
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