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A complex structure-preserving algorithm for split quaternion matrix LDU decomposition in split quaternion mechanics

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Abstract

Matrix decompositions play a prominent role in the theoretical study and numerical calculation of split quaternion mechanics. This paper, by means of a complex representation of split quaternion matrices, introduces Gaussian elimination of split quaternion matrices, and obtains a complex structure-preserving algorithm for split quaternion matrix LDU decomposition. Numerical examples show that the complex structure-preserving algorithm is more efficient.

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Authors and Affiliations

  1. Institute of Mathematics and Information Science, North-Eastern Federal University, Yakutsk, 677000, Russia

    Gang Wang & Tongsong Jiang

  2. School of Mathematics and Statistics, Heze University, Heze, Shandong, 274015, People’s Republic of China

    Gang Wang, Tongsong Jiang, Zhenwei Guo & Dong Zhang

  3. School of Mathematical Science, Liaocheng University, Liaocheng, Shandong, 252000, People’s Republic of China

    Tongsong Jiang & Zhenwei Guo

  4. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, 266590, People’s Republic of China

    Dong Zhang

Authors
  1. Gang Wang
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  2. Tongsong Jiang
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  3. Zhenwei Guo
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  4. Dong Zhang
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Correspondence to Tongsong Jiang.

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This paper is supported by the National Natural Science Foundation of China (No. 11771188), Chinese Government Scholarship (CSC No. 202008370340) and Shandong Natural Science Foundation (No. ZR201709250116).

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Wang, G., Jiang, T., Guo, Z. et al. A complex structure-preserving algorithm for split quaternion matrix LDU decomposition in split quaternion mechanics. Calcolo 58, 34 (2021). https://doi.org/10.1007/s10092-021-00424-7

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  • DOI: https://doi.org/10.1007/s10092-021-00424-7

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