求解弱双四元数矩阵方程r-循环解的新方法  

A new method for solving reduced biquaternion matrix equation r-circulant solution

作　　者：刘志红 李莹[1] 樊学玲 袭沂蒙 LIU Zhihong;LI Ying;FAN Xueling;XI Yimeng(School of Mathematical Sciences,Liaocheng University,Liaocheng 252000,Shandong,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252000

出　　处：《华中师范大学学报（自然科学版）》2023年第5期688-695,共8页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(62176112);山东省自然科学基金项目(ZR2020MA053,ZR2022MA030).

摘　　要：该文提出求解弱双四元数矩阵方程AX+XB=D的r-循环解及对称r-循环解的一种新方法.根据弱双四元数性质,利用vec算子把弱双四元数方程中变量X的位置统一变换到方程最后,然后根据弱双四元数的实表示方法将弱双四元数矩阵方程转化为实矩阵方程,再借助特殊矩阵的H-表示方法提取矩阵的独立元素参与运算,减少运算的复杂程度,通过数值试验检验了算法的有效性.最后将该文内容应用于采摘机器人手眼标定方法.A new method for solving the r-circulant solution and symmetric r-circulant solution of reduced biquaternion matrix equation AX+XB=D is proposed in this paper.According to the properties of reduced biquaternion,the vec operator is used to uniformly transform the position of variable X to the end of the reduced biquaternion equation.Then,the reduced biquaternion matrix equation is transformed into the real matrix equation according to the real representation method of reduced biquaternion.The independent elements of the matrix are extracted by using the H-representation method of special matrix to participate in the operation,which reduces the complexity of the operation.The effectiveness of the algorithm is verified by numerical experiments.Finally,the content of this paper is applied to the hand-eye calibration method of harvesting robot.

关 键 词：弱双四元数 实表示 H-表示 R-循环矩阵 

分 类 号：O241.6[理学—计算数学]