四元数等式约束最小二乘问题与四元数KKT方程的等价性  

EQUIVALENCE BETWEEN QUATERNION EQUALITY CONSTRAINED LEAST SQUARES PROBLEM AND QUATERNION KKT EQUATION

作　　者：张彦珍 李莹[1] 赵建立[1] 王刚 Zhang Yanzhen;Li Ying;Zhao Jianli;Wang Gang(School of Mathematical Science, Liaocheng University, Liaocheng 252000)

机构地区：[1]聊城大学数学科学学院

出　　处：《高等学校计算数学学报》2019年第3期234-243,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助(11301247)

摘　　要：1引言近年来,四元数和四元数矩阵方程在计算机图形学,量子物理,统计学,刚体力学,量子力学,控制论,场论,信号与彩色图像处理等学科中表现出巨大应用前景[1-5],随着应用范围的逐步拓广,许多学者对四元数产生了浓厚的兴趣,促使其理论和数值计算成果不断涌现[6,7]。In this paper, we study the equivalence problem of the quaternion equality constrained least squares problem. By using the properties of the generalized inverse of quaternion matrix and the quaternion orthogonal projection matrix, we prove the equivalence of the quaternion equality constrained least squares problem and the quaternion KKT equation. Therefore, the solution of the quaternion equality constrained least squares problem can be given based on the least squares solution of quaternion KKT equation.

关 键 词：QUATERNION EQUALITY constrained least SQUARES problem KKT equation equivalence 

分 类 号：O151.1[理学—数学]