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

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

Applied Mathematics and Computation, 2026, vol. 508, issue C

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.

Keywords: Sine-transform-based preconditioner; Approximate inverse preconditioner; Toeplitz-like systems (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003352

DOI: 10.1016/j.amc.2025.129609

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