Convergence analysis of TriCG and TriMR for symmetric quasi-definite linear systems

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.

arXiv comment18 pages, 3 figures