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矩阵特征空间和奇异空间相对扰动界 被引量:3

ADDITIVE RELATIVE PERTURBATION BOUNDS FOR EIGENSPACE AND SINGULAR SUBSPACE
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摘要 根据特征值和奇异值的相对分离情况,研究了矩阵特征空间和奇异空间的加法相对扰动界,得到一些新的扰动界. In term of the relative gaps of the eigenvalues and the singular values, the additive relative perturbation bounds of eigenspace and singular subspace of matrices are investigated and some new results are obtained.
作者 陈小山
出处 《华南师范大学学报(自然科学版)》 CAS 2005年第1期6-10,共5页 Journal of South China Normal University(Natural Science Edition)
基金 广东省自然科学基金资助项目(31496)
关键词 相对扰动界 特征空间 矩阵 奇异值 特征值 加法 eigenspace singular subspace relative perturbation bound angle matrix between subspaces
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参考文献2

  • 1LI Ren-cang. Relative perturbation theory:(Ⅱ) Eigenspace and singular subspace variations[J]. SIAM J Matrix Anal Appl, 1998, 20:471-492.
  • 2DOPICO F M, MORO J, MOLERA J M. Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices[J]. Linear Algebra and Its Applications, 2000, 309:3-18.

同被引文献15

  • 1王震,蔺小林,蒋耀林.行(或列)对称矩阵的满秩分解及其算法[J].高等学校计算数学学报,2005,27(S1):287-295. 被引量:13
  • 2Wedin P A. Perturbation bounds in connection with singular value decompostion [J]. BIT, 1972 (12) :99-111.
  • 3Li Ren-Cang. Relative perturbation theory. Eigenspace and singular subspace variations [J]. SIAM Matrir Anal. Appl, 1998,20:471-492.
  • 4Li R C.Relative perturbation theory(Ⅱ),Eigenspace and singular subspace variations,SIAM[J].Matrir Anal Appl,1999(20):471-492.
  • 5J Davis C,Kahan W.The rotation of eigenvectors by a perturbation(Ⅲ),SIAM[J].Numer.Anal,1970(7):1-46.
  • 6Li R C. Relative perturbation theory: I. Eigenvalue and singular value variations [ J ]. Siam Journal on Matrix A- nalysis and Applications, 1998,19:956 - 982.
  • 7Sun J G. Perturbation analysis of generalized singular subspaces[ J ]. Numerical Mathematics, 1998,79 : 615 - 641.
  • 8Chen X S. Two perturbation bounds for singular values and eigenvalues [ J ]. BIT Numerical Mathematics, 2008, 3:493 - 497.
  • 9Ipsen I C F, Nadler B. Refined perturbation bounds for ei- genvalues of Hermitian and non-Hermitian matrices [ J ]. Siam Journal on Matrix Analysis and Applications, 2009, 31:40 - 53.
  • 10Dickson K I, Kelley C T,Ipsen I C F,et al. Condition esti- mation for pseudo-arclength continuation[ J ]. S[AM Jour- nal on Numerical Analysis,2007,45:263 -276.

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