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Linear and Multilinear Algebra Volume 60, 2012 - Issue 8
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Original Articles

Relationship between the characteristic polynomial and the spectrum of a diagonalizable matrix and those of its low-rank update

Gang Wu School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116 Jiangsu, P.R. China
&
Yimin Wei School of Mathematical Sciences & Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai 200433, P.R. ChinaCorrespondence[email protected] [email protected]
Pages 967-978 | Received 13 May 2011, Accepted 26 Oct 2011, Published online: 16 Dec 2011

References

  • Chu , D and Chu , M . 2006 . Low-rank update of singualr values . Math. Comput. , 75 : 1351 – 1366 .
  • Cicone , A and Serra-Capizzano , S . 2010 . Google PageRanking problem: The model and the analysis . J. Comput. Appl. Math. , 234 : 3140 – 3169 .
  • da Fonseca , CM . 2007 . The characteristic polynomial of some perturbed tridiagonal k-Toeplitz matrices . Appl. Math. Sci. , 1 : 59 – 67 .
  • Ding , J and Yao , G . 2007 . The eigenvalue problem of a specially updated matrix . Appl. Math. Comput. , 185 : 415 – 420 .
  • Ding , J and Zhou , A . 2007 . Eigenvalues of rank-one updated matrices with some applications . Appl. Math. Lett. , 20 : 1223 – 1226 .
  • Eldén , L . The eigenvalues of the Google matrix . Tech. Rep. LiTH-MAT-R-2004-01, Linköping University ,
  • Golub , GH . 1973 . Some modified matrix eigenvalue problems . SIAM Rev. , 15 : 318 – 334 .
  • Golub , GH and Van Loan , CF . 1996 . Matrix Computations , 3rd , Baltimore and London : The Johns Hopkins University Press .
  • Gu , M and Eisenstat , S . 1995 . A divide-and-conquer algorithm for the symmetric tridiagonal eigenvalue problem . SIAM J. Matrix Anal. Appl. , 16 : 172 – 191 .
  • Horn , R and Serra-Capizzano , S . 2006 . A general setting for the parametric Google matrix . Internet. Math. , 3 : 385 – 411 .
  • Ipsen , I and Rehman , R . 2008 . Perturbation bounds for determinants and characteristic polynomials . SIAM J. Matrix Anal. Appl. , 30 : 762 – 776 .
  • G. Li and K. Yu, Adaptive rank-2 update algorithm for eigenvalue decomposition, IEEE Int. Conf. Acoust. Speech Signal Process. 3 (1988), pp. 1510–1513
  • Page , L , Brin , S , Motwami , R and Winograd , T . 1998 . The PageRank citation ranking: Bring order to the web , Tech. Rep., Computer Science Department, Stanford University .
  • Rehman , R . 2010 . “ Numerical computation of the characteristic polynomial of a complex matrix ” . In Ph.D. thesis , Raleigh , NC : North Carolina State University .
  • Rehman , R and Ipsen , I . 2011 . Computing characteristic polynomials from eigenvalues . SIAM J. Matrix Anal. Appl. , 32 : 90 – 114 .
  • Roy , S , Greenberg , B and Sarhan , A . 1960 . Evaluation of determinants, characteristic equations and their roots for a class of patterned matrices . J. Roy. Stat. Soc. Ser. B , 22 : 348 – 359 .
  • Steerneman , T and van Perlo-ten Kleij , F . 2005 . Properties of the matrix A − XY* . Linear Algebra Appl. , 410 : 70 – 86 .
  • Wu , G . 2008 . Eigenvalues and Jordan canonical form of a successively rank-one updated complex matrix with applications to Google's PageRank problem . J. Comput. Appl. Math. , 216 : 364 – 370 .
  • Xiong , Z and Zheng , B . 2009 . On the eigenvalues of a specially rank-r updated complex matrix . Comput. Math. Appl. , 57 : 1645 – 1650 .
  • Zhou , Y . 2011 . On the eigenvalues of specially low-rank perturbed matrices . Appl. Math. Comput. , 217 : 10267 – 10270 .

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