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.

中文翻译：

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分裂四元数力学中分裂四元数矩阵LDU分解的复杂保结构算法

矩阵分解在分裂四元数力学的理论研究和数值计算中发挥着重要作用。本文通过分裂四元数矩阵的复数表示，引入分裂四元数矩阵的高斯消元，得到分裂四元数矩阵LDU分解的复数保结构算法。数值例子表明复杂结构保持算法的效率更高。