QQMR: A Structure-Preserving Quaternion Quasi-Minimal Residual Method for Non-Hermitian Quaternion Linear Systems
CoRR(2024)
摘要
The quaternion biconjugate gradient (QBiCG) method, as a novel variant of
quaternion Lanczos-type methods for solving the non-Hermitian quaternion linear
systems, does not yield a minimization property. This means that the method
possesses a rather irregular convergence behavior, which leads to numerical
instability. In this paper, we propose a new structure-preserving quaternion
quasi-minimal residual method, based on the quaternion biconjugate
orthonormalization procedure with coupled two-term recurrences, which overcomes
the drawback of QBiCG. The computational cost and storage required by the
proposed method are much less than the traditional QMR iterations for the real
representation of quaternion linear systems. Some convergence properties of
which are also established. Finally, we report the numerical results to show
the robustness and effectiveness of the proposed method compared with QBiCG.
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