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Commun. Korean Math. Soc. 1995; 10(4): 981-995
Printed December 1, 1995
Copyright © The Korean Mathematical Society.
Convergence and breakdown study of krylov methods for nonsymmetric linear systems
Jae Heon Yun
Chungbuk National University
This paper first establishes some conditions for preconditioner under which PGCR does not break down. ~Next, VPGCR algorithm whose preconditioners can be easily obtained is introduced and then its breakdown and convergence properties are discussed. Lastly, implementation details of VPGCR are described and then numerical results of VPGCR with a certain criterion guaranteeing no breakdown are compared with those of restarted GMRES.
Keywords: Krylov method, breakdown, preconditioner
MSC numbers: 65F10
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