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关于矩阵LU分解的注记(英文) 被引量：2

Notes on LU-factorization of matrices
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摘要 本文主要研究了前n-1个顺序主子式均为非零的n阶方阵的LU分解.作者给出了这类矩阵的LU分解的具体表达式.该表达式由原矩阵中的元素和原矩阵的顺序主子阵的代数余子式给出.最后作者应用这个结果给出了Vandermonde矩阵及其转置矩阵LU分解的具体公式. The authors mainly investigate the LU factorization of the squate matrix of order n in which each of its first n-1 ordered principal minor is nonzero. An explicit expression of LU factorization of such matrices is proposed by using the elements of original matrices and algebraic cofactors in the or dered principal submatrices of the original matrix. Finally, applying this result, the authors give explicit formulas of the LU factc;rization of the Vandermonde matrix and its transpose.
作者 千国有 谭千蓉 王邦延
机构地区 四川大学数学学院 攀枝花学院计算机学院
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第2期273-278,共6页 Journal of Sichuan University(Natural Science Edition)
基金 国家自然科学基金(10971145) 高等学校博士学科点专项科研基金(20100181110073)
关键词 LU分解 VANDERMONDE矩阵 代数余子式 LU factorization, Vandermonde matrix, algebraic cofactors
分类号 O151.2 [理学—基础数学]
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参考文献11

  • 1Dresden A. On the generalized Vandermonde determinant and symmetric functions[J].Bulletin of the American Mathematical Society,1933.443.doi:10.1090/S0002-9904-1933-05664-1.
  • 2Horn R,Johnson C R. Matrix analysis[M].Cambridge:Cambridge University Press,1985.
  • 3Qian G Y,Lu J Y. LU-Factorizations of symmetric matrices with applications[J].Asian-European J Math,2010,(1):133.doi:10.1142/S179355711000009X.
  • 4Qruc H,Phillips G M. Explicit factorization of the Vandermonde matrix[J].Linear Algebra and Its Applications,2000,(1/3):113.doi:10.1016/S0024-3795(00)00124-5.
  • 5Yang S L. On the LU factorization of the Vandermonde matrix[J].Discrete Applied Mathematics,2005,(1):102.doi:10.1016/j.dam.2004.08.003.
  • 6Smith J.J. On the value of a certain arithmetical determinant[J].Proc Londom Math Soc,1875.208.
  • 7Hong S. On the Bourque-Ligh conjecture of least common multiple matrices[J].Algebra,1999,(1):216.doi:10.1006/jabr.1998.7844.
  • 8Hong S. Notes on power LCM matrices[J].Acta Arithmetica,2004.165.
  • 9Li M.Remarks on power LCM matrices on gcdclosed sets[J]四川大学学报(自然科学版),2007779.
  • 10Fang L.Notes on the Li-Cao conjecture on LCM equations[J]四川大学学报(自然科学版),2008467.

同被引文献18

  • 1潘晓峰,刘红星.基于神经网络的图像KL变换方法的改进[J].微处理机,2005,26(4):26-28. 被引量：5
  • 2冉瑞生,黄廷祝.三对角矩阵的逆[J].哈尔滨工业大学学报,2006,38(5):815-817. 被引量：15
  • 3Zamani J,Moghaddam A N,Rad H S.MRI reconstruction through Compressed Sensing using Principle Component Analysis (PCA)[C]// Proceedings of the 20th Iranian Conference on Electrical Engineering (ICEE).Tehran; IEEE,2012.
  • 4Du Q,Zhu W,Fowler J E.Anomaly Based Hyperspectral Image Compression[C]// Proceedings of IEEE International Conference on Geoscience andRemote Sensing Symposium (IGARSS).Boston,MA:IEEE,2008.
  • 5Oliveira P R,Romero R F'.A comparision between PCA neural networks and the JPEG standard for performing image compression[C]// Proceedings of Cybernetic Vision.Sao Carlos:IEEE,1996.
  • 6Lv C,Liu Z,Zhao Q.A flexible non-linear PCA encoder for still image compression[C]// Proceedings of 7th IEEE International Conference on Computer and Information Technology (CIT).Aizu-Wakamatsu,Fukushima:IEEE,2007.
  • 7Zhang Y,Mao Y.Convergence analysis of a deterministic discrete time system of Oja's PCA learning algorithm[J].IEEE Trans Nerual Netw,2005,16(3):1318.
  • 8Zhang D,Zhou Z H.Two directional two-dimensional PCA for efficient face representation and recognition[J].Elsevier,2005,69(3):224.
  • 9Mohammad M B,Mostafa M.A new technique for image compression using PCA[J].Int J Comput Sci,2012,2(1):111.
  • 10Santo R E.Principal component analysis applied to digital image compression[J].Einstein (Sāo Paulo),2012,10(2):135.

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二级引证文献13

四川大学学报（自然科学版）
2012年 第2期

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