A fast method for solving a block tridiagonal quasi-Toeplitz linear system

  • Skander Belhaj

    University of Tunis El Manar, Tunisia
  • Fahd Hcini

    University of Tunis El Manar, Tunisia
  • Yulin Zhang

    Universidade do Minho, Braga, Portugal
A fast method for solving a block tridiagonal quasi-Toeplitz linear system cover
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Abstract

This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [10], we propose a more general algorithm for such systems. The algorithm is based on a block decomposition for block tridiagonal quasi-Toeplitz matrices and the Sherman–Morrison–Woodbury inversion formula. We also compare the proposed approach to the standard block decomposition method and the Gauss algorithm. A theoretical error analysis is also presented. All algorithms have been implemented in Matlab. Numerical experiments performed on a wide variety of test problems show the effectiveness of our algorithm in terms of efficiency, stability and robustness.

Cite this article

Skander Belhaj, Fahd Hcini, Yulin Zhang, A fast method for solving a block tridiagonal quasi-Toeplitz linear system. Port. Math. 76 (2019), no. 3/4, pp. 287–299

DOI 10.4171/PM/2036