Convergence analysis of TriCG and TriMR for symmetric quasi-definite linear systems
Kui Du, Jia-Jun Fan
Abstract
TriCG and TriMR are two short-recurrence iterative methods introduced by Montoison and Orban [SIAM J.\ Sci.\ Comput., 43 (2021), pp.\ A2502--A2525] for solving symmetric quasi-definite linear systems. Extensive numerical experiments have demonstrated the efficiency of these two methods, but a systematic convergence analysis is still lacking. In this paper, we derive convergence bounds for the TriCG error norm and the TriMR residual norm. Numerical experiments support the theoretical results.
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