广义行(列)对称矩阵的QR分解及其算法  

QR factorization and algorithm for generalized row(column) symmetric matrix

作　　者：袁晖坪[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《计算机应用》2012年第4期990-993,998,共5页journal of Computer Applications

基　　金：重庆市自然科学基金资助项目(CSTS 2005 BB 0243);重庆市教委科学技术研究项目(KJ0707023)

摘　　要：对广义行(列)对称矩阵的QR分解和性质进行了研究,给出了广义行(列)对称矩阵的QR分解的公式和快速算法,它们可有效减少广义行(列)对称矩阵的QR分解的计算量与存储量,并且不会丧失数值精度。同时讨论了系统参数估计,推广和丰富了两文(邹红星,王殿军,戴琼海,等.行(或列)对称矩阵的QR分解.中国科学:A辑,2002,32(9):842-849;蔺小林,蒋耀林.酉对称矩阵的QR分解及其算法.计算机学报,2005,28(5):817-822)的研究内容,拓宽了实际应用领域的范围,并修正了后者的错误。The properties and the QR factorization of generalized row（column） symmetric matrix were studied,and some new results were gained.The formula and fast calculating way for the QR factorization of generalized row（column） symmetric matrix were obtained,and that formula could dramatically reduce the amount of calculation for QR factorization of generalized row（column） symmetric matrix,saved dramatically the CPU time and memory without loss of any numerical precision.Meanwhile,the system parameter estimation was discussed,some results of two paper（ZOU H,WANG D,DAI Q.et al.QR factorization for row or column symmetric matrix.Science of China： Series A,2002,32（9）： 842-849;LIN X L,JIANG Y L.QR Decomposition and Algorithm for Unitary Symmetric Matrix.Chinese Journal of Computers,2005,28（5）：817-822） were generalized,and some mistakes of the latter were corrected.

关 键 词：广义行(列)对称矩阵 QR分解 并行算法 信号处理 

分 类 号：TN911.7[电子电信—通信与信息系统]