四元数Cholesky分解的实保结构算法的再研究（英文）  

Real Structure-preserving Algorithms for the Quaternion Cholesky Decomposition:Revisit

作　　者：李莹[1] 魏木生 张凤霞[1] 赵建立[1] LI Ying;WEI Mu-sheng;ZHANG Feng-xia;ZHAO Jian-li(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China;School of Mathematics and Science,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059 [2]上海师范大学数理学院,上海200234

出　　处：《聊城大学学报（自然科学版）》2018年第1期21-28,共8页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(11301247,11171226);山东省教育厅科技项目(J15LI10)资助

摘　　要：文献[6]中,作者提出了四元数Cholesky分解的一种实保结构算法.本文对四元数Cholesky分解的实保结构算法进行了细致的研究,给出了基于高效运算的四元数Hermitian正定矩阵的LDL^H及LL^H分解的实保结构算法.我们将这两种实保结构算法的运算时间及精度与文献[6]中的算法及Matlab中的四元数工具包QTFM进行了比较.数值例子表明本文所提出的算法相对于利用低效运算[6]的算法及利用四元数代数运算的QTFM更加有效.In a paper published in 2013[6],Wang and Ma proposed a structure-preserving algorithm for computing the quaternion Cholesky decomposition.In this paper,we study the quaternion Cholesky decomposition carefully and re-propose real structure-preserving algorithms for LDLHand LLHdecompositions on quaternion Hermitian positive definite matrices,in which we make full use of high-level operations. We compared these real structure-preserving algorithms with the structure-preserving algorithm proposed by Wang and Ma[6]and Quaternion Toolbox for Matlab in terms of computational time and accuracy.Numerical experiments are provided to demonstrate that the qLDLH1 and qChol proposed in this paper are more efficient than algorithm of Wang and Ma using low-level operations and that in QTFM using quaternion arithmetics.

关 键 词：四元数矩阵 LDLH CHOLESKY分解 实表示 实保结构算法 

分 类 号：O151.21[理学—数学]