메뉴 건너뛰기




Volumn 46, Issue 4, 1999, Pages 327-359

General polynomial roots and their multiplicities in O(N) memory and O(N2) time

Author keywords

Complexity; DQR algorithm; Eigenvalue; Euclidean algorithm; Operations count; Polynomial root; Root multiplicity; Tridiagonal matrix

Indexed keywords


EID: 0346549071     PISSN: 03081087     EISSN: None     Source Type: Journal    
DOI: 10.1080/03081089908818625     Document Type: Article
Times cited : (9)

References (36)
  • 1
    • 0041953000 scopus 로고
    • Diskrete Verfahren zur Berechnung der Nullstellen von Polynomen
    • Bauhuber, F. (1970). Diskrete Verfahren zur Berechnung der Nullstellen von Polynomen, Computing, 5, 97-118.
    • (1970) Computing , vol.5 , pp. 97-118
    • Bauhuber, F.1
  • 3
    • 84963428213 scopus 로고
    • Numerical implementation of a new algorithm for polynomials with multiple roots
    • Brugnano, L. (1995). Numerical implementation of a new algorithm for polynomials with multiple roots, J. Difference Equ. Appl., 1, 187-207.
    • (1995) J. Difference Equ. Appl. , vol.1 , pp. 187-207
    • Brugnano, L.1
  • 4
    • 26444473141 scopus 로고    scopus 로고
    • Errata to: Numerical implementation of a new algorithm for polynomials with multiple roots
    • Brugnano, L. (1996). Errata to: Numerical implementation of a new algorithm for polynomials with multiple roots, J. Difference Equ. Appl., 2, 101.
    • (1996) J. Difference Equ. Appl. , vol.2 , pp. 101
    • Brugnano, L.1
  • 5
    • 21844508213 scopus 로고
    • Polynomial roots: The ultimate answer?
    • Brugnano, L. and Trigiante, D. (1995). Polynomial roots: the ultimate answer?, Lin. Alg. Appl., 225, 207-219.
    • (1995) Lin. Alg. Appl. , vol.225 , pp. 207-219
    • Brugnano, L.1    Trigiante, D.2
  • 6
    • 0030547039 scopus 로고    scopus 로고
    • A QL procedure for computing the eigenvalues of complex symmetric tridiagonal matrices
    • Cullum, J. K. and Willoughby, R. A. (1996). A QL procedure for computing the eigenvalues of complex symmetric tridiagonal matrices, SIAM J. Matr. Anal. Appl., 17, 83-109.
    • (1996) SIAM J. Matr. Anal. Appl. , vol.17 , pp. 83-109
    • Cullum, J.K.1    Willoughby, R.A.2
  • 7
    • 84968470212 scopus 로고
    • An algorithm for the machine calculation of complex Fourier series
    • Cooley, J. W. and Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series, Math. Comp., 19, 297-301.
    • (1965) Math. Comp. , vol.19 , pp. 297-301
    • Cooley, J.W.1    Tukey, J.W.2
  • 8
    • 0000659575 scopus 로고
    • A divide and conquer method for the symmetric tridiagonal eigenproblem
    • Cuppen, J. (1981). A divide and conquer method for the symmetric tridiagonal eigenproblem, Num. Math., 36, 177-195.
    • (1981) Num. Math. , vol.36 , pp. 177-195
    • Cuppen, J.1
  • 12
    • 84968482180 scopus 로고
    • Polynomial roots from companion matrix eigenvalues
    • Edelman, A, and Murakami, H. (1995). Polynomial roots from companion matrix eigenvalues, Math. Comp., 64, 763-776.
    • (1995) Math. Comp. , vol.64 , pp. 763-776
    • Edelman, A.1    Murakami, H.2
  • 15
    • 0009913239 scopus 로고
    • Expressing a polynomial as characteristic polynomial of a symmetric matrix
    • Fiedler, M. (1990). Expressing a polynomial as characteristic polynomial of a symmetric matrix, Lin. Alg. Appl., 141, 265-270.
    • (1990) Lin. Alg. Appl. , vol.141 , pp. 265-270
    • Fiedler, M.1
  • 17
    • 0000782325 scopus 로고
    • On the condition of algebraic equations
    • Gautschi, W. (1973). On the condition of algebraic equations, Num. Math., 21, 405-424.
    • (1973) Num. Math. , vol.21 , pp. 405-424
    • Gautschi, W.1
  • 18
    • 0006616766 scopus 로고
    • Remark on algorithms to find roots of polynomials
    • Goedecker, S. (1994). Remark on algorithms to find roots of polynomials, SIAM J. Sci. Comput., 15, 1059-1063.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1059-1063
    • Goedecker, S.1
  • 24
    • 38249003883 scopus 로고
    • A case against the divide and conquer approach to the nonsymmetric eigenvalue problem
    • Jessup, E. R. (1993). A case against the divide and conquer approach to the nonsymmetric eigenvalue problem, Appl. Num. Math., 12, 403-420.
    • (1993) Appl. Num. Math. , vol.12 , pp. 403-420
    • Jessup, E.R.1
  • 25
    • 84968487034 scopus 로고
    • A method for solving algebraic equations using an automatic computer
    • Muller, D. E. (1956). A method for solving algebraic equations using an automatic computer, Math. Tables Aids Comp., 10, 208-215.
    • (1956) Math. Tables Aids Comp. , vol.10 , pp. 208-215
    • Muller, D.E.1
  • 26
    • 0347505326 scopus 로고
    • Weyl's quadtree algorithm for the unsymmetric eigenvalue problem
    • Pan, V. Y. (1995). Weyl's quadtree algorithm for the unsymmetric eigenvalue problem, Appl. Math. Lett., 8, 87-88.
    • (1995) Appl. Math. Lett. , vol.8 , pp. 87-88
    • Pan, V.Y.1
  • 27
    • 0031169815 scopus 로고    scopus 로고
    • Solving the polynomial equation: Some history and recent progress
    • Pan, V. Y. (1997). Solving the polynomial equation: some history and recent progress, SIAM Review, 39, 187-220.
    • (1997) SIAM Review , vol.39 , pp. 187-220
    • Pan, V.Y.1
  • 29
    • 0345441668 scopus 로고
    • A real symmetric tridiagonal matrix with a given characteristic polynomial
    • Schmeisser, G. (1993). A real symmetric tridiagonal matrix with a given characteristic polynomial, Lin. Alg. Appl., 193, 11-18.
    • (1993) Lin. Alg. Appl. , vol.193 , pp. 11-18
    • Schmeisser, G.1
  • 30
    • 34250487811 scopus 로고
    • Gaussian elimination is not optimal
    • Strassen, V. (1969). Gaussian elimination is not optimal, Num. Math., 13, 354-356.
    • (1969) Num. Math. , vol.13 , pp. 354-356
    • Strassen, V.1
  • 31
    • 0039286659 scopus 로고
    • Another look at a matrix of Marc Kac
    • Taussky, O. and Todd, J. (1991). Another look at a matrix of Marc Kac, Lin. Alg. Appl., 150, 341-360.
    • (1991) Lin. Alg. Appl. , vol.150 , pp. 341-360
    • Taussky, O.1    Todd, J.2
  • 32
    • 26444614696 scopus 로고
    • Are the coefficients of a polynomial well-conditioned functions of its roots?
    • Uhlig, F. (1992). Are the coefficients of a polynomial well-conditioned functions of its roots? Num. Math., 61, 383-393.
    • (1992) Num. Math. , vol.61 , pp. 383-393
    • Uhlig, F.1
  • 33
    • 0031487023 scopus 로고    scopus 로고
    • The DQR algorithm, basic theory, convergence and conditional stability
    • Uhlig, F. (1997). The DQR algorithm, basic theory, convergence and conditional stability, Num. Math., 76, 515-553.
    • (1997) Num. Math. , vol.76 , pp. 515-553
    • Uhlig, F.1
  • 34
    • 21844503637 scopus 로고
    • Forward stability and transmission of shifts in the QR algorithm
    • Watkins, D. S. (1995). Forward stability and transmission of shifts in the QR algorithm, SIAM J. Matrix Anal. Appl., 16, 467-487.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 467-487
    • Watkins, D.S.1
  • 35
    • 34250946236 scopus 로고
    • Randbemerkungen zu Hauptproblemen der Algebra, II, Fundamentalsatz der Algebra und Grundlagen der Mathematik
    • Weyl, H. (1924). Randbemerkungen zu Hauptproblemen der Algebra, II, Fundamentalsatz der Algebra und Grundlagen der Mathematik, Math. Z., pp. 131-151.
    • (1924) Math. Z. , pp. 131-151
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.