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

作　　者：王敏 

机构地区：[1]贺州学院公共基础教学部,广西 贺州

出　　处：《应用数学进展》2022年第8期5660-5668,共9页Advances in Applied Mathematics

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。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.

关 键 词：四元数 双Hermite矩阵 奇异值分解 反问题 

分 类 号：O151.21[理学—数学]