Abstract
(p,q)-Pentadiagonal matrices have received considerable attention in recent years, which are a generalization of pentadiagonal matrices. In this paper, a breakdown-free algorithm is presented for numerically evaluating the determinants of n-by-n (p,q)-pentadiagonal matrices. The algorithm is based on the use of a reliable tridiagonalization process which preserves the banded structure and sparsity of the original matrix. Numerical examples are given in order to illustrate the effectiveness of the proposed algorithm. All of the experiments are performed on a computer with the aid of programs written in MATLAB.
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The authors would like to thank the anonymous referees for their valuable comments and suggestions that substantially enhanced the quality of the manuscript.
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Ji-Teng Jia: conceived, designed and performed the analysis; Prepared the manuscript. Rong Xie: performed the numerical analysis and wrote the manuscript. Shuo Ni: performed the numerical experiments. Xiao-Yan Xu: contributed analysis tools.
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Jia, JT., Xie, R., Ni, S. et al. An efficient breakdown-free algorithm for numerically evaluating the determinants of (p, q)-pentadiagonal matrices. Numer Algor 97, 2031–2049 (2024). https://doi.org/10.1007/s11075-024-01777-0
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DOI: https://doi.org/10.1007/s11075-024-01777-0