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<p>Inspired by the regularized and the SIMPLE-like preconditioners for block two-by-two saddle point problems, we propose a new preconditioner called regularized SIMPLE-like (RSL) preconditioner for solving a class of double saddle point problems in block three-by-three form. Through theoretical analyses, the compact distribution areas of the real and non-real eigenvalues, and other spectral properties of the RSL preconditioned matrix are obtained. Moreover, we derive a practical approach to the parameters involved. Numerical experiments show that the RSL preconditioners have satisfactory performance in accelerating Krylov subspace methods.</p>

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Regularized SIMPLE-like preconditioners for double saddle point problems

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Yan Dou,
  • Yuan-Fan Bai

摘要

Inspired by the regularized and the SIMPLE-like preconditioners for block two-by-two saddle point problems, we propose a new preconditioner called regularized SIMPLE-like (RSL) preconditioner for solving a class of double saddle point problems in block three-by-three form. Through theoretical analyses, the compact distribution areas of the real and non-real eigenvalues, and other spectral properties of the RSL preconditioned matrix are obtained. Moreover, we derive a practical approach to the parameters involved. Numerical experiments show that the RSL preconditioners have satisfactory performance in accelerating Krylov subspace methods.