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<p>Structured quaternion linear systems have emerged as a research focus in engineering and scientific computations, particularly the structure-preserving quaternion generalized minimal residual (QGMRES) method for solving quaternion linear systems arising from color image restoration problems. In this paper, we investigate fast algorithms for the solution of quaternion linear systems <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Ax = b\)</EquationSource> </InlineEquation>. We propose a modified QGMRES method tailored to systems with structured coefficient matrices, which substantially enhances the convergence rate of the underlying iterative process. Numerical experiments performed on both synthetic datasets and real-world color image restoration tasks demonstrate that the superiority of the proposed algorithms over existing methods.</p>

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Preconditioned generalized minimal residual method for quaternion linear systems with structured coefficient matrices and its applications

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Chengyu Hu,
  • Wenxv Ding,
  • Ying Li

摘要

Structured quaternion linear systems have emerged as a research focus in engineering and scientific computations, particularly the structure-preserving quaternion generalized minimal residual (QGMRES) method for solving quaternion linear systems arising from color image restoration problems. In this paper, we investigate fast algorithms for the solution of quaternion linear systems \(Ax = b\) . We propose a modified QGMRES method tailored to systems with structured coefficient matrices, which substantially enhances the convergence rate of the underlying iterative process. Numerical experiments performed on both synthetic datasets and real-world color image restoration tasks demonstrate that the superiority of the proposed algorithms over existing methods.