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Improved analysis of sine-transform-based approximate inverse preconditioner for Toeplitz-like systems

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  • Fang, Zhi-Wei
  • Li, Tian-Yi
  • Sun, Hai-Wei
  • Sun, Tao

Abstract

An approximate inverse preconditioner based on sine transform is considered for the nonsymmetric linear systems with diagonal-times-Toeplitz structure, where the Toeplitz matrix is symmetric positive definite. With some assumptions on the elements of the Toeplitz matrix, we proved that the spectra of the preconditioned matrix are located in a bounded interval around one. This result supports the efficiency of the preconditioner more strongly than the former results with low-rank parts, especially in high-dimensional cases. Numerical results are presented to confirm the efficiency of the proposed preconditioner.

Suggested Citation

  • Fang, Zhi-Wei & Li, Tian-Yi & Sun, Hai-Wei & Sun, Tao, 2026. "Improved analysis of sine-transform-based approximate inverse preconditioner for Toeplitz-like systems," Applied Mathematics and Computation, Elsevier, vol. 508(C).
    • Handle: RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003352
    DOI: 10.1016/j.amc.2025.129609
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