四元数体上一类矩阵方程解的数值方法  

Numerical methods on a kind of linear matrix equation systems over quaternion field

作　　者：邓勇[1] 黄敬频[2] 

机构地区：[1]喀什师范学院数学系,新疆喀什844006 [2]广西民族大学数学与计算机科学学院,广西南宁530006

出　　处：《纯粹数学与应用数学》2010年第5期705-709,共5页Pure and Applied Mathematics

基　　金：新疆高校科研基金(XJEDU2008I31)

摘　　要：建立了求解四元数体上严格对角占优矩阵方程AX=B的QJ和QSOR迭代方法,并利用四元数矩阵的右特征值最大模刻画出迭代的收敛性,给出参数的取值范围;最后运用四元数矩阵的复表示运算保结构的特性,把这两种迭代等价地转化到复数域上,从而实现了该系统的数值求解.In this paper, the QJ and QSOR iterative algorithms of the strictly diagonally dominant linear systems AX = B over quaternion field are structured, and convergence of the two algorithms are described by using right eigenvalue maximum norm of the quaternion matrix, and the optimal range of parameters are obtained. Meanwhile, applying the structure preserving property of the complex representation operation of the quaternion matrix, QJ and QSOR are transformed into the iteration over complex field, thus realizes numerical solutions of the linear systems.

关 键 词：四元数矩阵 严格对角占优 QJ和QSOR迭代 右特征值最大模 

分 类 号：O151.21[理学—数学]