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Volumn Part F129620, Issue , 1992, Pages 195-205

Real algebraic number computation using interval arithmetic

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EID: 84974685232     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/143242.143311     Document Type: Conference Paper
Times cited : (9)

References (24)
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    • Akritas, A.1    Collins, G.E.2
  • 3
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    • The minimum root separation of a polynomial
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  • 5
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    • Polynomial real root isolation by differentiation
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    • (1976) Proceedings of SYMSAC 76 , pp. 15-25
    • Collins, G.E.1    Loos, R.2
  • 6
    • 0010932815 scopus 로고
    • Infallible calculation of polynomial zeros to specified precision
    • Academic Press, Inc., New York, San Francisco and London
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    • (1977) Mathematical Software III
    • Collins, G.E.1
  • 7
    • 85031699122 scopus 로고
    • Rutgers workshop on symbolic software for mathematical research, March
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    • (1991) Announcement of SAC2-C System
    • Collins, G.E.1
  • 8
    • 0001560099 scopus 로고
    • Thorn's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets
    • [CR88] M. Coste and M. F. Roy. Thorn's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets. Journal of Symbolic Computation, 5(1, 2):121-129, 1988.
    • (1988) Journal of Symbolic Computation , vol.5 , Issue.1-2 , pp. 121-129
    • Coste, M.1    Roy, M.F.2
  • 10
    • 0001345156 scopus 로고
    • On condition numbers and the distance to the nearest ill-posed problem
    • [Dem87] James W. Demmel. On Condition Numbers and the Distance to the Nearest Ill-posed Problem. Numerische Mathematik, 51:251-289, 1987.
    • (1987) Numerische Mathematik , vol.51 , pp. 251-289
    • Demmel, J.W.1
  • 11
    • 0042902761 scopus 로고
    • A globally convergent interval method for computing and bounding real roots
    • [Han78] Eldon Hansen. A globally convergent interval method for computing and bounding real roots. BIT, 18:415-424, 1978.
    • (1978) BIT , vol.18 , pp. 415-424
    • Hansen, E.1
  • 13
    • 0003896049 scopus 로고
    • Technical Report, Department of Computer and Information Science, The Ohio State University, August, Ph. D. Thesis
    • [Joh91] J. R. Johnson. Algorithms for polynomial real root isolation. Technical Report OSU-CISRC-8/91-TR21, Department of Computer and Information Science, The Ohio State University, August 1991. Ph. D. Thesis.
    • (1991) Algorithms for Polynomial Real Root Isolation
    • Johnson, J.R.1
  • 14
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    • An inequality for the discriminant of a polynomial
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    • (1964) Michigan Mathematics Journal , vol.11 , Issue.3 , pp. 257-262
    • Mahler, K.1
  • 16
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    • Interval Analysis
    • Prentice-Hall, Inc., Engle-wood Cliffs, N. J.
    • [m0066] R. E. Moore. Interval Analysis. Series in Automatic Computation. Prentice-Hall, Inc., Engle-wood Cliffs, N. J., 1966.
    • (1966) Series in Automatic Computation
    • Moore, R.E.1
  • 17
    • 0003717416 scopus 로고
    • Methods and applications of interval arithmetic
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    • [Moo79] R. E. Moore. Methods and Applications of Interval Arithmetic. Studies in Applied Mathematics. SIAM, 1979.
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  • 19
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    • Complexity of computation of real algebraic numbers
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  • 22
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    • (1988) Trends in Computer Algebra, Volume 296 of Lecture Notes in Computer Science , pp. 177-197
    • Rump, S.M.1
  • 23
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    • Quasi-GCD computations
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    • (1985) Journal of Complexity , vol.1 , pp. 118-137
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  • 24
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    • The evaluation of the zeros of ill-conditioned polynomials, parts i and II
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