메뉴 건너뛰기




Volumn 100, Issue 3, 2005, Pages 373-408

Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84947068118     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-005-0595-4     Document Type: Article
Times cited : (81)

References (60)
  • 1
    • 0039715485 scopus 로고
    • QR-like algorithms for symmetric arrow matrices
    • Arbenz, P., Golub, G.H.: QR-like algorithms for symmetric arrow matrices. SIAM J. Matrix Anal. Appl. 13(2), 655-658 (1992)
    • (1992) SIAM J. Matrix Anal. Appl , vol.13 , Issue.2 , pp. 655-658
    • Arbenz, P.1    Golub, G.H.2
  • 2
    • 0039742542 scopus 로고
    • Matrix shapes invariant under the symmetric QR algorithm
    • Arbenz, P., Golub, G.H.: Matrix shapes invariant under the symmetric QR algorithm. Numer. Linear Algebra Appl. 2, 87-93 (1995)
    • (1995) Numer. Linear Algebra Appl , vol.2 , pp. 87-93
    • Arbenz, P.1    Golub, G.H.2
  • 4
    • 0016598313 scopus 로고
    • Acompanion matrix analogue for orthogonal polynomials
    • Barnett, S.:Acompanion matrix analogue for orthogonal polynomials. LinearAlgebra and Appl. 12(3), 197-208 (1975)
    • (1975) Linearalgebra and Appl , vol.12 , Issue.3 , pp. 197-208
    • Barnett, S.1
  • 5
  • 6
    • 1242307407 scopus 로고    scopus 로고
    • Inverse power and Durand-Kerner iterations for univariate polynomial root-finding
    • Bini, D.A., Gemignani, L., Pan, V.Y.: Inverse power and Durand-Kerner iterations for univariate polynomial root-finding. Comput. Math. with Appl. 47, 447-459 (2004)
    • (2004) Comput. Math. with Appl , vol.47 , pp. 447-459
    • Bini, D.A.1    Gemignani, L.2    Pan, V.Y.3
  • 7
    • 23344445986 scopus 로고    scopus 로고
    • Improved initialization of the accelerated and robust QR-like polynomial root-finding
    • Bini, D.A., Gemignani, L., Pan, V.Y.: Improved initialization of the accelerated and robust QR-like polynomial root-finding, Electron. Trans. Numer. Anal. 17, 195-205 (2004)
    • (2004) Electron. Trans. Numer. Anal , vol.17 , pp. 195-205
    • Bini, D.A.1    Gemignani, L.2    Pan, V.Y.3
  • 9
    • 21344495471 scopus 로고
    • Iteration schemes for the divide-and-conquer eigenvalue solver
    • Bini, D., Gemignani, L.: Iteration schemes for the divide-and-conquer eigenvalue solver. Numer. Math. 67, 403-425 (1994)
    • (1994) Numer. Math , vol.67 , pp. 403-425
    • Bini, D.1    Gemignani, L.2
  • 10
    • 34250270918 scopus 로고
    • Updating the singular value decomposition
    • Bunch, J.R., Nielsen, C.P.: Updating the singular value decomposition. Numer. Math. 31, 111-129 (1978)
    • (1978) Numer. Math , vol.31 , pp. 111-129
    • Bunch, J.R.1    Nielsen, C.P.2
  • 11
    • 0002316189 scopus 로고
    • Rank-one modification of the symmetric eigenproblem
    • Bunch, J.R., Nielsen, C.P., Sorensen, D.C.: Rank-one modification of the symmetric eigenproblem. Numer. Math. 31, 31-48 (1978)
    • (1978) Numer. Math , vol.31 , pp. 31-48
    • Bunch, J.R.1    Nielsen, C.P.2    Sorensen, D.C.3
  • 12
    • 0037114693 scopus 로고    scopus 로고
    • The restarted QR-algorithm for eigenvalue computation of structured matrices
    • Calvetti, D., Kim, S., Reichel, L.: The restarted QR-algorithm for eigenvalue computation of structured matrices. J. Comput. Appl. Math. 149, 415-422 (2002)
    • (2002) J. Comput. Appl. Math , vol.149 , pp. 415-422
    • Calvetti, D.1    Kim, S.2    Reichel, L.3
  • 13
    • 1242336491 scopus 로고
    • Linear construction of companion matrices
    • Carstensen, C.: Linear construction of companion matrices. Linear Algebra Appl. 149, 191-214 (1991)
    • (1991) Linear Algebra Appl , vol.149 , pp. 191-214
    • Carstensen, C.1
  • 14
    • 0034394306 scopus 로고    scopus 로고
    • Fast and stable eigendecomposition of symmetric banded plus semiseparable matrices
    • Chandrasekaran, S., Gu, M.: Fast and stable eigendecomposition of symmetric banded plus semiseparable matrices. Linear Algebra Appl. 313, 107-114 (2000)
    • (2000) Linear Algebra Appl , vol.313 , pp. 107-114
    • Chandrasekaran, S.1    Gu, M.2
  • 17
    • 0000659575 scopus 로고    scopus 로고
    • A divide and conquer method for the symmetric tridiagonal eigenproblem
    • (1980/81)
    • Cuppen, J.J.M.: A divide and conquer method for the symmetric tridiagonal eigenproblem. Numer. Math. 36, 177-195 (1980/81)
    • Numer. Math , vol.36 , pp. 177-195
    • Cuppen, J.1
  • 21
    • 0000417182 scopus 로고
    • Afully parallel algorithm for the symmetric eigenvalue problem
    • Dongarra, J.J., Sorensen, D.C.: Afully parallel algorithm for the symmetric eigenvalue problem. SIAM J. Sci. Stat. Comput. 8, 139-154 (1987)
    • (1987) SIAM J. Sci. Stat. Comput , vol.8 , pp. 139-154
    • Dongarra, J.J.1    Sorensen, D.C.2
  • 22
    • 0031071241 scopus 로고    scopus 로고
    • " Inversion formulas and linear complexity algorithm for diagonal plus semiseparable matrices
    • Eidelman, Y., Gohberg, I:" Inversion formulas and linear complexity algorithm for diagonal plus semiseparable matrices. Comput. Math. Appl. 33, 69-79 (1997)
    • (1997) Comput. Math. Appl , vol.33 , pp. 69-79
    • Eidelman, Y.1    Gohberg, I.2
  • 24
    • 31244431952 scopus 로고    scopus 로고
    • A modification of the Dewilde-van der Veen method for inversion of finite structured matrices
    • Eidelman, Y., Gohberg, I.: A modification of the Dewilde-van der Veen method for inversion of finite structured matrices. LinearAlgebraAppl. 343-344, 419-450 (2002)
    • (2002) Linearalgebraappl , vol.343 , pp. 419-450
    • Eidelman, Y.1    Gohberg, I.2
  • 25
    • 0042090490 scopus 로고    scopus 로고
    • Fast inversion algorithms for a class of structured operator matrices
    • Eidelman, Y., Gohberg, I.: Fast inversion algorithms for a class of structured operator matrices. Linear Algebra Appl. 371, 153-190 (2003)
    • (2003) Linear Algebra Appl , vol.371 , pp. 153-190
    • Eidelman, Y.1    Gohberg, I.2
  • 26
    • 0001329073 scopus 로고
    • A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin’s theorem
    • Elsner, L.: A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin’s theorem. Numer. Math. 21, 425-427 (1973)
    • (1973) Numer. Math , vol.21 , pp. 425-427
    • Elsner, L.1
  • 28
    • 0142077182 scopus 로고    scopus 로고
    • Structural and computational properties of possibly singular semiseparable matrices
    • Fasino, D., Gemignani, L.: Structural and computational properties of possibly singular semiseparable matrices. Linear Algebra Appl. 340, 183-198 (2002)
    • (2002) Linear Algebra Appl , vol.340 , pp. 183-198
    • Fasino, D.1    Gemignani, L.2
  • 30
    • 0009913239 scopus 로고
    • Expressing a polynomial as the characteristic polynomial of a symmetric matrix
    • Fiedler, M.: Expressing a polynomial as the characteristic polynomial of a symmetric matrix. Linear Algebra Appl. 141, 265-270 (1990)
    • (1990) Linear Algebra Appl , vol.141 , pp. 265-270
    • Fiedler, M.1
  • 31
    • 0036335550 scopus 로고    scopus 로고
    • An iterated eigenvalue algorithm for approximating roots of univariate polynomials
    • Fortune, S.: An iterated eigenvalue algorithm for approximating roots of univariate polynomials. J. Symbolic Comput. 33(5), 627-646 (2002)
    • (2002) J. Symbolic Comput , vol.33 , Issue.5 , pp. 627-646
    • Fortune, S.1
  • 32
    • 0000288741 scopus 로고
    • An algorithm for subspace computation with applications in signal processing
    • Fuhrmann, D.R.: An algorithm for subspace computation with applications in signal processing. SIAM J. Matrix Anal. Appl. 9, 213-220 (1988)
    • (1988) SIAM J. Matrix Anal. Appl , vol.9 , pp. 213-220
    • Fuhrmann, D.R.1
  • 33
    • 0019370951 scopus 로고
    • Least squares with a quadratic constraint
    • Gander, W.: Least squares with a quadratic constraint. Numer. Math. 36, 291-307 (1981)
    • (1981) Numer. Math , vol.36 , pp. 291-307
    • Gander, W.1
  • 37
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • Golub, G.H.: Some modified matrix eigenvalue problems. SIAM Rev. 15, 318-334 (1973)
    • (1973) SIAM Rev , vol.15 , pp. 318-334
    • Golub, G.H.1
  • 39
    • 0001678475 scopus 로고
    • Quadratically constrained least squares and quadratic problems
    • Golub, G.H., von Matt, U.: Quadratically constrained least squares and quadratic problems. Numer. Math. 59, 561-580 (1991)
    • (1991) Numer. Math , vol.59 , pp. 561-580
    • Golub, G.H.1    Von Matt, U.2
  • 40
    • 38249042117 scopus 로고
    • The QR algorithm for unitary Hessenberg matrices
    • Gragg, W.B.: The QR algorithm for unitary Hessenberg matrices. J. Comput. Appl. Math. 16, 1-8 (1986)
    • (1986) J. Comput. Appl. Math , vol.16 , pp. 1-8
    • Gragg, W.B.1
  • 41
    • 0031460710 scopus 로고    scopus 로고
    • Linear complexity algorithm for semiseparable matrices
    • Koltracht, I.: Linear complexity algorithm for semiseparable matrices. Integral Equations Operator Theory 29(3), 313-319 (1997)
    • (1997) Integral Equations Operator Theory , vol.29 , Issue.3 , pp. 313-319
    • Koltracht, I.1
  • 42
    • 0003066775 scopus 로고
    • A composite polynomial zerofinding matrix algorithm
    • Malek, F., Vaillancourt, R.: A composite polynomial zerofinding matrix algorithm. Comput. Math. Appl. 30(2), 37-47 (1995)
    • (1995) Comput. Math. Appl , vol.30 , Issue.2 , pp. 37-47
    • Malek, F.1    Vaillancourt, R.2
  • 44
    • 84879517390 scopus 로고
    • Numerical solution of a secular equation
    • Melman, A.: Numerical solution of a secular equation. Numer. Math. 69, 483-493 (1995)
    • (1995) Numer. Math , vol.69 , pp. 483-493
    • Melman, A.1
  • 45
    • 0031540780 scopus 로고    scopus 로고
    • A unifying convergence analysis of second-order methods for secular equations
    • Melman, A.: A unifying convergence analysis of second-order methods for secular equations. Math. Comp. 66, 333-344 (1997)
    • (1997) Math. Comp , vol.66 , pp. 333-344
    • Melman, A.1
  • 46
    • 0038909659 scopus 로고
    • Cleve’s Corner: ROOTS - Of polynomials, that is
    • Moler, C.: Cleve’s Corner: ROOTS - Of polynomials, that is. The MathWorks Newsletter 5(1), 8-9 (1991)
    • (1991) The Mathworks Newsletter , vol.5 , Issue.1 , pp. 8-9
    • Moler, C.1
  • 47
    • 38249017274 scopus 로고
    • Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices
    • O’Leary, D.P., Stewart, G.W.: Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices. J. Comput. Phys. 90(2), 497-505 (1990)
    • (1990) J. Comput. Phys , vol.90 , Issue.2 , pp. 497-505
    • O’Leary, D.P.1    Stewart, G.W.2
  • 49
    • 85041034226 scopus 로고    scopus 로고
    • Preprint no. 1181, November 1993, IMA - Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA
    • Solomonoff, A.: Application of multipole methods to two matrix eigenproblems. Preprint no. 1181, November 1993, IMA - Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA
    • Application of Multipole Methods to Two Matrix Eigenproblems
    • Solomonoff, A.1
  • 51
    • 0346549071 scopus 로고    scopus 로고
    • General polynomial roots and their multiplicities in O(N) memory and O(n2) time
    • Uhlig, F.: General polynomial roots and their multiplicities in O(n) memory and O(n2) time. Linear and Multilinear Algebra 46(4), 327-359 (1999)
    • (1999) Linear and Multilinear Algebra , vol.46 , Issue.4 , pp. 327-359
    • Uhlig, F.1
  • 52
    • 0031487023 scopus 로고    scopus 로고
    • The DQR algorithm, basic theory, convergence, and conditional stability
    • Uhlig, F.: The DQR algorithm, basic theory, convergence, and conditional stability. Numer. Math. 76(4), 515-553 (1997)
    • (1997) Numer. Math , vol.76 , Issue.4 , pp. 515-553
    • Uhlig, F.1
  • 53
    • 85041070898 scopus 로고    scopus 로고
    • Technical Report TW350, Katholieke Universiteit Leuven, Department Computerwetenschappen, Submitted to SIAM J. Matrix Anal. Appl
    • Van Barel, M., Fasino, D., Gemignani, L., Mastronardi, N.: Orthogonal rational functions. Technical Report TW350, Katholieke Universiteit Leuven, Department Computerwetenschappen, 2002. Submitted to SIAM J. Matrix Anal. Appl.
    • (2002) Orthogonal Rational Functions
    • van Barel, M.1    Fasino, D.2    Gemignani, L.3    Mastronardi, N.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.