Abstract
As a generalization of k-tridiagonal matrices, many variations of (p,q)-tridiagonal matrices have attracted much attention over the years. In this paper, we present an efficient algorithm for numerically computing the inverses of n-square (p,q)-tridiagonal matrices under a certain condition. The algorithm is based on the combination of a bidiagonalization approach which preserves the banded structure and sparsity of the original matrix, and a recursive algorithm for inverting general lower bidiagonal matrices. Some numerical results with simulations in MATLAB implementation are provided in order to illustrate the accuracy and efficiency of the proposed algorithms, and its competitiveness with MATLAB built-in function.
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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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This work was supported by the Natural Science Foundation of China (NSFC) under grant 11601408 and the Fundamental Research Funds for the Central Universities under grant JB210720 and YJS2223.
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Rong Xie, Xiao-Yan Xu, Shuo Ni, and Jie Wang contributed equally to this work.
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Jia, JT., Xie, R., Xu, XY. et al. A bidiagonalization-based numerical algorithm for computing the inverses of (p,q)-tridiagonal matrices. Numer Algor 93, 899–917 (2023). https://doi.org/10.1007/s11075-022-01446-0
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DOI: https://doi.org/10.1007/s11075-022-01446-0