泛延拓矩阵的QR分解
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摘要
考虑泛延拓矩阵的QR分解与广义逆,导出了泛延拓矩阵的QR分解与广义逆的公式,讨论了系统参数估计问题.结果显示所给方法既减少了计算量与存储量,又不会降低数值精度.同时推广和优化了文献[8,9]的研究结果,拓宽了实际应用领域的范围.
The author studied the QR factorization and generalized inverse of universal extended matrix. and the system parameter estimate is discussed. In addition, the formula of the QR factorization and generalized inverse of universal extended matrix were given. The results show that the algorithm is simple and fast, and it does not reduce the numerical accuracy.Another some results of paper[8,9]are generalized.
The author studied the QR factorization and generalized inverse of universal extended matrix. and the system parameter estimate is discussed. In addition, the formula of the QR factorization and generalized inverse of universal extended matrix were given. The results show that the algorithm is simple and fast, and it does not reduce the numerical accuracy.Another some results of paper[8,9]are generalized.
引文
[1]PARLETT B. N. The QR algorithm[J]. Computing in Sci-ence&Engineering,2000,2(1):38-42.
[2] PRASAD S. Direction-of-arrival estimation using rank re-vealing QR factorization[J]. IEEE Trans Signal Process-ing,1991,39(5):1224-1229.
[3] LI X. QR factorization based blind channel identificationand equalization w ith second-order statistics[J]. IEEETrans. Signal Processing,2000,48(1):60-69.
[4]ZAROWSKI C J,MA X,FAIRMAN F W. QR-factorizationmethod for computing the greatest common divisor of poly-nomials w ith inexact coefficients[J]. IEEE Trans SignalProcessing,2000,48(11):3042-3051.
[5]HUAJUN HUANG,TIN-YAU TAM. An asymptotic behav-ior of QR decomposition[J]. Linear Algebra and Its Appli-cations. 2007,424(2):96-107.
[6] Chang Xiaowen,Paige C C,Stewart G W. Perturbation a-nalysis for the QR factorization[J]. SIAM J M atrix AnalAppl,1997,18(2):775-791.
[7]Stewart,G. W. Error analysis of QR updating with exponen-tial w indow ing[J],M ath. Comp.,1992,199(1):135-140.
[8]邹红星,王殿军,戴琼海,等.行(或列)对称矩阵的QR分解[J].中国科学(A辑),2002,32(9):842-849.Zou H-X,Wang D-J,Dai Q-H et al. QR factorization forrow or column symmetric matrix[J]. Science of China(Series A),2002,32(9)842-849.(in Chinese)
[9]蔺小林,蒋耀林.酉对称矩阵的QR分解及其算法[J].计算机学报,2005,28(5):818-822.LIN Xiao-Lin,JIANG Yao-Lin. QR decomposition and al-gorithm for unitary symmetric matrix[J]. Chinese Journalof Computers,2005,28(5):818-822.(in Chinese)
[10]丛进,杨绿溪.基于QR分解的MIMO信道盲辨识和盲均衡方法[J].电子学报,2004,32(10):1589-1593.CONG Jin,YANG Lu xi. Blind identification and blind e-qualization of M IM O channels based on QR factorization[J]. Acta Mathematica Sinica,2004,32(10):1589-1593.(in Chinese)
[11]张贤达.矩阵分析与应用[M].北京:清华大学出版社,2004. 9.Zhang X-D. M atrix Analysis and Applications[M]. Bei-jing:Tsinghua University Press,2004. 9.(in Chinese)
[12]刘永辉,田永革.矩阵广义逆的一个混合反序律[J].数学学报,2009,52(01):197-204.Liu Y-H,Tian Y-G. A mixed-type reverse order law forgeneralized inverse of a triple matrix product[J]. ActaM athematica Sinica,2009,52(01):197-204.(in Chi-nese)
[13]邹红星,王殿军,戴琼海,李衍达.延拓矩阵的奇异值分解[J].电子学报,2001,29(3):290-292.ZOU Hong xing,WANG Dian jun,DAI Qiong hai,LI Yanda. Singular value decomposition for extended matrix[J].Acta Electronica Sinica,2001,29(3):290-292.(in Chi-nese)
[14]袁晖坪.泛延拓矩阵的奇异值分解[J].电子学报,2012,40(8):1539-1543.YUAN Hui-ping. Singular value factorization for universalextended matrix[J]. Acta Electronica Sinica,2012,40(8):1539-1543.(in Chinese)
[2] PRASAD S. Direction-of-arrival estimation using rank re-vealing QR factorization[J]. IEEE Trans Signal Process-ing,1991,39(5):1224-1229.
[3] LI X. QR factorization based blind channel identificationand equalization w ith second-order statistics[J]. IEEETrans. Signal Processing,2000,48(1):60-69.
[4]ZAROWSKI C J,MA X,FAIRMAN F W. QR-factorizationmethod for computing the greatest common divisor of poly-nomials w ith inexact coefficients[J]. IEEE Trans SignalProcessing,2000,48(11):3042-3051.
[5]HUAJUN HUANG,TIN-YAU TAM. An asymptotic behav-ior of QR decomposition[J]. Linear Algebra and Its Appli-cations. 2007,424(2):96-107.
[6] Chang Xiaowen,Paige C C,Stewart G W. Perturbation a-nalysis for the QR factorization[J]. SIAM J M atrix AnalAppl,1997,18(2):775-791.
[7]Stewart,G. W. Error analysis of QR updating with exponen-tial w indow ing[J],M ath. Comp.,1992,199(1):135-140.
[8]邹红星,王殿军,戴琼海,等.行(或列)对称矩阵的QR分解[J].中国科学(A辑),2002,32(9):842-849.Zou H-X,Wang D-J,Dai Q-H et al. QR factorization forrow or column symmetric matrix[J]. Science of China(Series A),2002,32(9)842-849.(in Chinese)
[9]蔺小林,蒋耀林.酉对称矩阵的QR分解及其算法[J].计算机学报,2005,28(5):818-822.LIN Xiao-Lin,JIANG Yao-Lin. QR decomposition and al-gorithm for unitary symmetric matrix[J]. Chinese Journalof Computers,2005,28(5):818-822.(in Chinese)
[10]丛进,杨绿溪.基于QR分解的MIMO信道盲辨识和盲均衡方法[J].电子学报,2004,32(10):1589-1593.CONG Jin,YANG Lu xi. Blind identification and blind e-qualization of M IM O channels based on QR factorization[J]. Acta Mathematica Sinica,2004,32(10):1589-1593.(in Chinese)
[11]张贤达.矩阵分析与应用[M].北京:清华大学出版社,2004. 9.Zhang X-D. M atrix Analysis and Applications[M]. Bei-jing:Tsinghua University Press,2004. 9.(in Chinese)
[12]刘永辉,田永革.矩阵广义逆的一个混合反序律[J].数学学报,2009,52(01):197-204.Liu Y-H,Tian Y-G. A mixed-type reverse order law forgeneralized inverse of a triple matrix product[J]. ActaM athematica Sinica,2009,52(01):197-204.(in Chi-nese)
[13]邹红星,王殿军,戴琼海,李衍达.延拓矩阵的奇异值分解[J].电子学报,2001,29(3):290-292.ZOU Hong xing,WANG Dian jun,DAI Qiong hai,LI Yanda. Singular value decomposition for extended matrix[J].Acta Electronica Sinica,2001,29(3):290-292.(in Chi-nese)
[14]袁晖坪.泛延拓矩阵的奇异值分解[J].电子学报,2012,40(8):1539-1543.YUAN Hui-ping. Singular value factorization for universalextended matrix[J]. Acta Electronica Sinica,2012,40(8):1539-1543.(in Chinese)