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Volumn 12, Issue 4, 1996, Pages 572-594

On isolation of real and nearly real zeros of a univariate polynomial and its splitting into factors

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EID: 0030498361     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.1996.0034     Document Type: Article
Times cited : (5)

References (30)
  • 2
    • 0001761077 scopus 로고
    • Evaluating polynomials at fixed set of points
    • [ASU75] AHO, A. V., STEIGLITZ, K., and ULLMAN, J. D. (1975), Evaluating polynomials at fixed set of points, SIAM J. Comput. 4, 533-539.
    • (1975) SIAM J. Comput. , vol.4 , pp. 533-539
    • Aho, A.V.1    Steiglitz, K.2    Ullman, J.D.3
  • 5
    • 0030512509 scopus 로고    scopus 로고
    • Graeffe's, Chebyshev-like, and Cardinal's processes for splitting a polynomial into factors
    • [BPb] BINI, D., and PAN, V. Y. (1996), Graeffe's, Chebyshev-like, and Cardinal's processes for splitting a polynomial into factors, J. of Complexity 12, 492-511.
    • (1996) J. of Complexity , vol.12 , pp. 492-511
    • Bini, D.1    Pan, V.Y.2
  • 7
    • 84968518922 scopus 로고
    • A numerical method for locating zeros of an analytic function
    • [DL67] DELVES, L. M., and LYNESS, J. N., (1967), A numerical method for locating zeros of an analytic function, Math. Comput. 21, 543-560.
    • (1967) Math. Comput. , vol.21 , pp. 543-560
    • Delves, L.M.1    Lyness, J.N.2
  • 8
    • 0015082322 scopus 로고
    • The simultaneous improvement of a complete set of approximate factors of a polynomial
    • [G71] GRAU, A. A. (1971), The simultaneous improvement of a complete set of approximate factors of a polynomial, SIAM J. Numer. Anal. 8, 425-438.
    • (1971) SIAM J. Numer. Anal. , vol.8 , pp. 425-438
    • Grau, A.A.1
  • 9
    • 0000082767 scopus 로고
    • Norm estimates for the inverses of Vandermonde matrices
    • [Ga75] GAUTSCHI, W. (1975), Norm estimates for the inverses of Vandermonde matrices, Numer. Math. 23, 337-347.
    • (1975) Numer. Math. , vol.23 , pp. 337-347
    • Gautschi, W.1
  • 10
    • 0000846903 scopus 로고
    • How (un)stable are Vandermonde systems?
    • "Intern. Symp. on Asymptotic and Computational Analysis: Conference in Honor Frank W. J. Olver's 65th Birthday (R. Wong, Ed.), Decker, New York
    • [Ga90] GAUTSCHI, W. (1990), How (un)stable are Vandermonde systems?, in "Intern. Symp. on Asymptotic and Computational Analysis: Conference in Honor Frank W. J. Olver's 65th Birthday (R. Wong, Ed.), Lecture Notes in Pure and Applied Math., Vol. 124, pp. 193-210, Decker, New York.
    • (1990) Lecture Notes in Pure and Applied Math. , vol.124 , pp. 193-210
    • Gautschi, W.1
  • 11
    • 84966207762 scopus 로고
    • A fast algorithm for the multiplication of generalized Hilbert matrix by vector
    • [Ge87] Gerasoulis, A. (1987), A fast algorithm for the multiplication of generalized Hilbert matrix by vector, Math. Comput. 50(181), 179-188.
    • (1987) Math. Comput. , vol.50 , Issue.181 , pp. 179-188
    • Gerasoulis, A.1
  • 14
    • 0001046726 scopus 로고
    • Generalization of an algorithm of Sebastiao e Silva
    • [Ho71] Householder, A. S. (1971), Generalization of an algorithm of Sebastiao e Silva, Numer. Math. 16, 375-382.
    • (1971) Numer. Math. , vol.16 , pp. 375-382
    • Householder, A.S.1
  • 17
    • 51649212837 scopus 로고
    • Recherches sur la méthode de graeffe et les zéros des polynomes et des series de laurent
    • [O40] OSTROWSKI, A. M. (1940), Recherches sur la Méthode de Graeffe et les Zéros des Polynomes et des Series de Laurent, Acta Math. 72, 99-257.
    • (1940) Acta Math. , vol.72 , pp. 99-257
    • Ostrowski, A.M.1
  • 18
    • 0023592849 scopus 로고
    • Sequential and parallel complexity of approximate evaluation of polynomial zeros
    • [P87] Pan, V. Y. (1987), Sequential and parallel complexity of approximate evaluation of polynomial zeros, Comput. Math. Appl. 14(8), 591-622.
    • (1987) Comput. Math. Appl. , vol.14 , Issue.8 , pp. 591-622
    • Pan, V.Y.1
  • 19
    • 0001116810 scopus 로고
    • Fast evaluation and interpolation at the Chebyshev set of points
    • [P89] PAN, V. Y. (1989), Fast evaluation and interpolation at the Chebyshev set of points, Appl. Math. Lett. 2(3), 255-258.
    • (1989) Appl. Math. Lett. , vol.2 , Issue.3 , pp. 255-258
    • Pan, V.Y.1
  • 20
    • 0028255188 scopus 로고
    • New techniques for approximating complex polynomial zeros
    • ACM Press, New York, and SIAM, Philadelphia
    • [P94] PAN, V. Y. (1994), New techniques for approximating complex polynomial zeros, in "Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms," pp. 260-270, ACM Press, New York, and SIAM, Philadelphia.
    • (1994) Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms , pp. 260-270
    • Pan, V.Y.1
  • 21
    • 0002333206 scopus 로고
    • Optimal (up to polylog factors) sequential and parallel algorithms for approximating complex polynomial zeros
    • ACM Press, New York
    • [P95] PAN, V. Y. (1995), Optimal (up to polylog factors) sequential and parallel algorithms for approximating complex polynomial zeros, in "Proc. 27th Ann. ACM Symp. on Theory of Computing," pp. 741-750, ACM Press, New York.
    • (1995) Proc. 27th Ann. ACM Symp. on Theory of Computing , pp. 741-750
    • Pan, V.Y.1
  • 22
    • 0029346257 scopus 로고
    • Deterministic improvement of complex polynomial factorization based on the properties of associated resultant
    • [P95a] PAN, V. Y. (1995), Deterministic improvement of complex polynomial factorization based on the properties of associated resultant, Comput. Math. Appl. 30(2), 237-250.
    • (1995) Comput. Math. Appl. , vol.30 , Issue.2 , pp. 237-250
    • Pan, V.Y.1
  • 24
    • 0030168306 scopus 로고    scopus 로고
    • Optimal and nearly optimal algorithms for approximating polynomial zeros
    • [P96a] PAN, V. Y. (1996), Optimal and nearly optimal algorithms for approximating polynomial zeros, Comput. Math. Appl. 31(12), 97-138.
    • (1996) Comput. Math. Appl. , vol.31 , Issue.12 , pp. 97-138
    • Pan, V.Y.1
  • 25
    • 0031169815 scopus 로고    scopus 로고
    • Solving a polynomial equation: Some history and recent progress
    • [P,a] PAN, V. Y. (to appear), Solving a polynomial equation: Some history and recent progress, SIAM Rev. 39, 1.
    • SIAM Rev. , vol.39 , pp. 1
    • Pan, V.Y.1
  • 27
    • 0000151023 scopus 로고
    • Quasi-GCD computations
    • [Sc85] SCHÖNHAGE, A. (1985), Quasi-GCD computations, J. Complexity 1, 118-137.
    • (1985) J. Complexity , vol.1 , pp. 118-137
    • Schönhage, A.1
  • 28
    • 0011476649 scopus 로고
    • Uber das Newtonsche Verfahren
    • [Schr57] SCHRÖDER, J. (1957), Uber das Newtonsche Verfahren, Arch. Rational Mech. Anal. 1, 154-180.
    • (1957) Arch. Rational Mech. Anal. , vol.1 , pp. 154-180
    • Schröder, J.1
  • 29
    • 0001164080 scopus 로고
    • Sur une Méthode d' Approximation Semblable à Celle de Graeffe
    • [SeS41] SEBASTIAO E SILVA, J. (1941), Sur une Méthode d' Approximation Semblable à Celle de Graeffe, Portugal Math. 2, 271-279.
    • (1941) Portugal Math. , vol.2 , pp. 271-279
    • Sebastiao E Silva, J.1
  • 30
    • 0011463433 scopus 로고
    • Upper bounds for roots of polynomials
    • [VdS70] VAN DER SLUIS, A. (1970), Upper bounds for roots of polynomials, Numer. Math. 15, 250-262.
    • (1970) Numer. Math. , vol.15 , pp. 250-262
    • Van Der Sluis, A.1


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