Abstract
Due to the increasing applications of dual quaternion and their matrices in recent years, as well as the significance of LU decomposition as a matrix decomposition technique, in this paper, we propose dual quaternion Gaussian transformation and obtain dual quaternion LU decomposition by using Gaussian transformation. We also use the total order of dual numbers to obtain the partial pivoting dual quaternion LU decomposition. Based on the real structure-preserving algorithm of quaternion matrix, we propose the real structure-preserving algorithms of LU decomposition and partial pivoting LU decomposition for dual quaternion matrix. Numerical experiments have verified the effectiveness of the new real structure-preserving approaches.
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We thank the referees for providing detailed and valuable comments and suggestions, which are very helpful for improving our paper.
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This work is supported by the National Natural Science Foundation of China under grants 62176112, the Natural Science Foundation of Shandong Province under grant ZR2020MA053, ZR2022MA030, and the Discipline with Strong Characteristics of Liaocheng University–Intelligent Science and Technology under grant 319462208.
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Wang, T., Li, Y., Wei, M. et al. Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01753-8
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DOI: https://doi.org/10.1007/s11075-024-01753-8