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<p>This paper introduces inexact versions of several block-splitting preconditioners for solving the three-by-three block linear systems arising from a special class of indefinite least squares problems. We first establish the convergence conditions for the corresponding stationary iterative methods. Then, it follows that under these conditions, all eigenvalues of the preconditioned matrices are contained within a circle centered at (1,&#xa0;0) with radius 1. This property implies that these preconditioners are effective in accelerating the convergence of the GMRES method. Furthermore, we analyze the eigenpairs of the preconditioned matrices in detail and derive a theoretical upper bound on the number of GMRES iterations for solving the preconditioned systems. Ultimately, numerical experiments reveal the efficacy of the proposed preconditioners.</p>

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Inexact versions of several block-splitting preconditioners for indefinite least squares problems

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Mohaddese Kaveh Shaldehi,
  • Davod Khojasteh Salkuyeh

摘要

This paper introduces inexact versions of several block-splitting preconditioners for solving the three-by-three block linear systems arising from a special class of indefinite least squares problems. We first establish the convergence conditions for the corresponding stationary iterative methods. Then, it follows that under these conditions, all eigenvalues of the preconditioned matrices are contained within a circle centered at (1, 0) with radius 1. This property implies that these preconditioners are effective in accelerating the convergence of the GMRES method. Furthermore, we analyze the eigenpairs of the preconditioned matrices in detail and derive a theoretical upper bound on the number of GMRES iterations for solving the preconditioned systems. Ultimately, numerical experiments reveal the efficacy of the proposed preconditioners.