On Igmres(q): Incomplete Generalized Minimal Residual Methods for Large Unsymmetric Linear Systems

Content Provider	Semantic Scholar
Author	Jiay, Zhongxiao
Copyright Year	1994
Abstract	In this paper, we analyze in detail incomplete generalized minimal residual methods (IGMRES(q)), proposed by Brown et al., for solving large unsymmetric linear systems, which are truncated versions of the generalized minimal residual method (GMRES), and establish a convergence theory of the methods. We derive the relationship between the residual norms for IGMRES(q) and GMRES, and expose that IGMRES(q) can work well and behave much like GMRES under the assumption that the basis vectors of Krylov subspace generated by IGMRES(q) are strongly linearly independent. Also, we establish some relationships between the residual norms for IOMs(q) and IGMRES(q). Theoretical analysis shows that IGMRES(q) may not behave like GMRES since the basis vectors generated by IGMRES(q) can be nearly linearly dependent for any unsymmetric matrix and the parameter q. As for practical considerations, we suggest one strategy of choosing q. Finally, some numerical experiments are reported to show convergence behaviors of IGMRES(q) and their restarted versions.
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Alternate Webpage(s)	http://www.mathematik.uni-bielefeld.de/sfb343/preprints/pr94047.ps.gz
Language	English
Access Restriction	Open
Subject Keyword	Basis (linear algebra) Behavior Choose (action) Convergence (action) Experiment Generalized minimal residual method Krylov subspace Linear system Numerical analysis Partial Population Parameter Version
Content Type	Text
Resource Type	Article