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Volumn 26, Issue 3, 2005, Pages 599-620

On symmetric eigenproblems induced by the bidiagonal SVD

Author keywords

Bidiagonal SVD; Coupling relations; Relatively robust representations; Stability

Indexed keywords

ALGORITHMS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); VECTORS;

EID: 22944479035     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479801394829     Document Type: Article
Times cited : (6)

References (23)
  • 2
    • 0012066317 scopus 로고
    • Decomposition of a symmetric matrix
    • J. BUNCH, L. KAUFMAN, AND B. PARLETT, Decomposition of a symmetric matrix, Numer. Math., 27 (1976), pp. 95-107.
    • (1976) Numer. Math. , vol.27 , pp. 95-107
    • Bunch, J.1    Kaufman, L.2    Parlett, B.3
  • 4
    • 0001192187 scopus 로고
    • Accurate singular values of bidiagonal matrices
    • J. DEMMEL AND W. KAHAN, Accurate singular values of bidiagonal matrices, SIAM J. Sci. Stat. Comput., 11 (1990), pp. 873-912.
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 873-912
    • Demmel, J.1    Kahan, W.2
  • 5
    • 33144470575 scopus 로고    scopus 로고
    • The accurate and efficient solution of a totally positive generalized Vandermonde linear system
    • to appear
    • J. DEMMEL AND P. KOEV, The accurate and efficient solution of a totally positive generalized Vandermonde linear system, SIAM J. Matrix Anal. Appl., to appear.
    • SIAM J. Matrix Anal. Appl.
    • Demmel, J.1    Koev, P.2
  • 6
    • 21144468781 scopus 로고
    • Jacobi's method is more accurate than QR
    • J. DEMMEL AND K. VESELIĆ, Jacobi's method is more accurate than QR, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 1204-1245.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 1204-1245
    • Demmel, J.1    Veselić, K.2
  • 7
    • 0039504477 scopus 로고    scopus 로고
    • Fernando's solution to Wilkinson's problem: An application of double factorization
    • I. DHILLON AND B. PARLETT, Fernando's solution to Wilkinson's problem: An application of double factorization, Linear Algebra Appl., 267 (1997), pp. 247-279.
    • (1997) Linear Algebra Appl. , vol.267 , pp. 247-279
    • Dhillon, I.1    Parlett, B.2
  • 8
    • 2942514399 scopus 로고    scopus 로고
    • Orthogonal eigenvectors and relative gaps
    • I. S. DHILLON AND B. N. PARLETT, Orthogonal eigenvectors and relative gaps, SIAM J. Matrix Anal. Appl., 25 (2004), pp. 858-899.
    • (2004) SIAM J. Matrix Anal. Appl. , vol.25 , pp. 858-899
    • Dhillon, I.S.1    Parlett, B.N.2
  • 9
    • 0034421232 scopus 로고    scopus 로고
    • Relatively robust representations for symmetric tridiagonals
    • I. DHILLON AND B. PARLETT, Relatively robust representations for symmetric tridiagonals, Linear Algebra Appl., 309 (2000), pp. 121-151.
    • (2000) Linear Algebra Appl. , vol.309 , pp. 121-151
    • Dhillon, I.1    Parlett, B.2
  • 11
    • 21344465239 scopus 로고    scopus 로고
    • Computing an eigenvector of a tridiagonal when the eigenvalue is known
    • K. FERNANDO, Computing an eigenvector of a tridiagonal when the eigenvalue is known, Z. Angew. Math. Mech., 76 (1996), pp. 299-302.
    • (1996) Z. Angew. Math. Mech. , vol.76 , pp. 299-302
    • Fernando, K.1
  • 12
    • 0031536846 scopus 로고    scopus 로고
    • On computing an eigenvector of a tridiagonal matrix. Part I: Basic results
    • K. V. FERNANDO, On computing an eigenvector of a tridiagonal matrix. Part I: Basic results, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 1013-1034.
    • (1997) SIAM J. Matrix Anal. Appl. , vol.18 , pp. 1013-1034
    • Fernando, K.V.1
  • 13
    • 0032216897 scopus 로고    scopus 로고
    • Accurately counting singular values of bidiagonal matrices and eigenvalues of skew-symmetric tridiagonal matrices
    • K. V. FERNANDO, Accurately counting singular values of bidiagonal matrices and eigenvalues of skew-symmetric tridiagonal matrices, SIAM J. Matrix Anal. Appl., 20 (1998), pp. 373-399.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.20 , pp. 373-399
    • Fernando, K.V.1
  • 14
    • 21344496407 scopus 로고
    • Accurate singular values and differential qd algorithms
    • K. FERNANDO AND B. PARLETT, Accurate singular values and differential qd algorithms, Numer. Math., 67 (1994), pp. 191-229.
    • (1994) Numer. Math. , vol.67 , pp. 191-229
    • Fernando, K.1    Parlett, B.2
  • 16
    • 22944478947 scopus 로고
    • Computation of an eigenvector of a symmetric tridiagonal matrix
    • S. GODUNOV, V. KOSTIN, AND A. MITCHENKO, Computation of an eigenvector of a symmetric tridiagonal matrix, Siberian Math. J., 26 (1985), pp. 684-696.
    • (1985) Siberian Math. J. , vol.26 , pp. 684-696
    • Godunov, S.1    Kostin, V.2    Mitchenko, A.3
  • 19
    • 84862379808 scopus 로고    scopus 로고
    • 2) algorithm for the bidiagonal SVD
    • 2) algorithm for the bidiagonal SVD, Linear Algebra Appl., 358 (2003), pp. 45-70.
    • (2003) Linear Algebra Appl. , vol.358 , pp. 45-70
    • Grosser, B.1    Lang, B.2
  • 20
    • 0034379502 scopus 로고    scopus 로고
    • An implementation of the dqds algorithm (positive case)
    • O. MARQUES AND B. PARLETT, An implementation of the dqds algorithm (positive case), Linear Algebra Appl., 309 (2000), pp. 217-259.
    • (2000) Linear Algebra Appl. , vol.309 , pp. 217-259
    • Marques, O.1    Parlett, B.2
  • 21
    • 0010843126 scopus 로고
    • Der Quotienten-Differenzen-Algorithmus
    • H. RUTISHAUSER, Der Quotienten-Differenzen-Algorithmus, Z. Angew. Math. Phys., 5 (1954), pp. 233-251.
    • (1954) Z. Angew. Math. Phys. , vol.5 , pp. 233-251
    • Rutishauser, H.1
  • 22
    • 0003301233 scopus 로고
    • Computational frameworks for the fast fourier transform
    • SIAM, Philadelphia
    • C. VAN LOAN, Computational Frameworks for the Fast Fourier Transform, Frontiers Appl. Math. 10, SIAM, Philadelphia, 1992.
    • (1992) Frontiers Appl. Math. , vol.10
    • Van Loan, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.