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<p>In this paper, we study the least-squares problem for semi-infinite Toeplitz and quasi-Toeplitz matrices. By exploiting the structural properties of Toeplitz matrices and employing the Wiener–Hopf factorization of the associated generating function, we develop an efficient iterative method for solving the problem. We also provide a sufficient condition to guarantee the convergence of the proposed algorithm. For numerical implementation, we apply a finite section method that approximates semi-infinite Toeplitz matrices by their finite-rank projections.</p>

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Least-squares problem on infinite Toeplitz and quasi-Toeplitz systems

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Elham Nobari,
  • Bijan Ahmadi Kakavandi

摘要

In this paper, we study the least-squares problem for semi-infinite Toeplitz and quasi-Toeplitz matrices. By exploiting the structural properties of Toeplitz matrices and employing the Wiener–Hopf factorization of the associated generating function, we develop an efficient iterative method for solving the problem. We also provide a sufficient condition to guarantee the convergence of the proposed algorithm. For numerical implementation, we apply a finite section method that approximates semi-infinite Toeplitz matrices by their finite-rank projections.