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<p>According to the structure of the discrete linear system derived from the considered two-dimensional Riesz space-fractional diffusion equations, the <i>banded preconditioner with adjustable shift compensation</i> (<b>BASC preconditioner</b>) is constructed to accelerate the convergence rate of the Krylov subspace iteration methods by compensating the banded truncation of the coefficient matrix with a parameterized shift matrix. When the parameter is 1, the BASC preconditioner is exactly the existing <i>banded preconditioner with shift compensation</i> (<b>BSC preconditioner</b>). In addition, by selecting an appropriate parameter close to 1, the BASC preconditioner can outperform the BSC preconditioner or achieve comparable performance, which can be confirmed through asymptotic singular value or eigenvalue analysis as well as numerical experiments.</p>

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Spectral analysis of the banded preconditioning with adjustable shift compensation for solving two-dimensional Riesz space-fractional diffusion equations

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Ying Sun,
  • Kang-Ya Lu,
  • Zong-Han Li,
  • Jun-Heng Niu,
  • Yu-Fan Cao

摘要

According to the structure of the discrete linear system derived from the considered two-dimensional Riesz space-fractional diffusion equations, the banded preconditioner with adjustable shift compensation (BASC preconditioner) is constructed to accelerate the convergence rate of the Krylov subspace iteration methods by compensating the banded truncation of the coefficient matrix with a parameterized shift matrix. When the parameter is 1, the BASC preconditioner is exactly the existing banded preconditioner with shift compensation (BSC preconditioner). In addition, by selecting an appropriate parameter close to 1, the BASC preconditioner can outperform the BSC preconditioner or achieve comparable performance, which can be confirmed through asymptotic singular value or eigenvalue analysis as well as numerical experiments.