TY  - GEN 
T1  - On the admissible convergence curves for restarted GMRES
A1  - Duintjer Tebbens, Jurjen
A1  - Meurant, Gérard
Y1  - 2014
N2  - This paper studies admissible convergence curves for restarted GMRES and their relation to the curves for full GMRES. It shows that stagnation at the end of a restart cycle is mirrored at the beginning of the next cycle. Otherwise, any non-increasing convergence curve is possible and pairs {A, b} are constructed such that when restarted GMRES is applied to Ax = b, prescribed residual norms and Ritz values for the individual cycles are generated. Additionally, A can have any spectrum. The constructed systems lead to full GMRES processes that can be generated with short recurrences and offer some insight into the phenomenon of larger restart lengths being able to result in slower convergence.
M1  - Preprint project = NCMM
M1  - Preprint year = 2014
M1  - Preprint number = 23
M1  - Preprint ID = NCMM/2014/23
ER  -