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<p>This paper further extends the shift-splitting (SS) and local shift-splitting (LSS) preconditioners to solve the general block two-by-two linear systems. We demonstrate that the eigenvalues of the corresponding preconditioned matrices cluster tightly around 2 by detailed spectral property analysis. Numerical experiments not only validate the theoretical results but also show the effectiveness and superiority of the SS and LSS preconditioners by comparing them with some existing preconditioners applied to the generalized minimal residual (GMRES) method for solving the block two-by-two linear systems.</p>

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A Class of Shift-Splitting Preconditioners for Solving the General Block Two-by-Two Linear Systems

  • 期刊论文

  • 发表日期：

    2025年6月18日

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  • Yu-Lan Liu,
  • Bo Wu

摘要

This paper further extends the shift-splitting (SS) and local shift-splitting (LSS) preconditioners to solve the general block two-by-two linear systems. We demonstrate that the eigenvalues of the corresponding preconditioned matrices cluster tightly around 2 by detailed spectral property analysis. Numerical experiments not only validate the theoretical results but also show the effectiveness and superiority of the SS and LSS preconditioners by comparing them with some existing preconditioners applied to the generalized minimal residual (GMRES) method for solving the block two-by-two linear systems.