四元数体上双Hermite矩阵反问题的最小二乘解

Least-Squares Solution to the Dou-ble-Hermite Matrix Inverse Problem on the Quaternion Field

摘要: 讨论四元数体上的矩阵方程组AX = Z，Y*A = W*的双Hermite矩阵反问题的最小二乘解及其最佳逼近解。利用双Hermite矩阵的结构特性及奇异值分解定理，将原问题转化为Hermite矩阵方程问题，得出该问题解的表达式。最后给出数值算例检验算法的正确、可行。

Abstract: To discuss the least-squares solution and the best approximation solution of the double-Hermite matrix inverse problem of the matrix equation system AX = Z, Y*A = W* on the quaternion field. The original problem is transformed into an equation problem with Hermite matrix structure by using the structural properties of double-Hermite matrices and the singular value decomposition theo-rem. The expression for the solution to the problem is obtained. Finally, a numerical example is given to test the correctness and feasibility of the algorithm.