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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.
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BibTeX
@misc{du2026convergence,
title = {{Convergence analysis of TriCG and TriMR for symmetric quasi-definite linear systems}},
author = {Kui Du and Jia-Jun Fan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04189},
eprint = {2611.04189},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04189},
}
RIS
TY - UNPB
TI - Convergence analysis of TriCG and TriMR for symmetric quasi-definite linear systems
AU - Kui Du
AU - Jia-Jun Fan
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04189
UR - https://arxiv.org/abs/2611.04189
AB - 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.
ER -