A fast and efficient iterative method for solving some class of Toeplitz linear equations systems

Bijan Ahmadi Kakavandi and Elham Nobari – GJM, Volume 9, Issue 2 (2024), 1-9.

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• décembre 25, 2024
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We present an innovative and straightforward algorithm designed for solving a class of linear equations systems A \mathrm{x}=\mathrm{y} where A is an n \times n Toeplitz matrix. Whenever the symbol function of the Toeplitz matrix A remains away from zero, our method enables us to efficiently approximate the system’s solution, utilizing only O(n \log n) arithmetic operations. This iterative approach involves expanding the original matrix by incorporating an associated circulant matrix and exploiting the properties of the symbol function to compute its inverse.

Milestones:

Received: November 7, 2024
Accepted: December 14, 2024
Revised: December 15, 2024

Authors:

Bijan Ahmadi Kakavandi
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
Shahid Beheshti University, Tehran, Iran
Elham Nobari
Department of Mathematics,
University of Science and Technology of Mazandaran, Behshahr, Iran.

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