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Volumn 1644 LNCS, Issue , 1999, Pages 55-73

Real computations with fake numbers

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

EID: 22644449122     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48523-6_5     Document Type: Conference Paper
Times cited : (5)

References (36)
  • 1
    • 0030291482 scopus 로고    scopus 로고
    • On the combinatorial and algebraic complexity of quantifier elimination
    • S. Basu, R. Pollack, and M.-F. Roy. On the combinatorial and algebraic complexity of quantifier elimination. Journal of the ACM, 43:1002-1045, 1996.
    • (1996) Journal of the ACM , vol.43 , pp. 1002-1045
    • Basu, S.1    Pollack, R.2    Roy, M.-F.3
  • 3
    • 84968516134 scopus 로고
    • On a theory of computation and complexity over the real numbers: Np-completeness, recursive functions and universal machines
    • L. Blum, M. Shub, and S. Smale. On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines. Bulletin of the Amer. Math. Soc., 21:1-46, 1989.
    • (1989) Bulletin of the Amer. Math. Soc. , vol.21 , pp. 1-46
    • Blum, L.1    Shub, M.2    Smale, S.3
  • 6
    • 0043284645 scopus 로고    scopus 로고
    • Complexity estimates depending on condition and round off error
    • To appear
    • F. Cucker and S. Smale. Complexity estimates depending on condition and round off error. To appear in Journal of the ACM, 1997.
    • (1997) Journal of the ACM
    • Cucker, F.1    Smale, S.2
  • 7
    • 0001427559 scopus 로고
    • Towards a formal definition of numerical stability
    • L.S. de Jong. Towards a formal definition of numerical stability. Numer. Math., 28:211-219, 1977.
    • (1977) Numer. Math. , vol.28 , pp. 211-219
    • De Jong, L.S.1
  • 9
    • 0000802374 scopus 로고
    • The approximation of one matrix by another of lower rank
    • C. Eckart and G. Young. The approximation of one matrix by another of lower rank. Psychometrika, 1:211-218, 1936.
    • (1936) Psychometrika , vol.1 , pp. 211-218
    • Eckart, C.1    Young, G.2
  • 13
    • 0003245845 scopus 로고
    • Seminumerical Algorithms, Addison-Wesley, 2 edition
    • D. Knuth. The Art of Computer Programming, volume 2, Seminumerical Algorithms. Addison-Wesley, 2 edition, 1981.
    • (1981) The Art of Computer Programming , vol.2
    • Knuth, D.1
  • 14
    • 84887430394 scopus 로고    scopus 로고
    • The real dimension problem is npir-complete
    • To appear in
    • P. Koiran. The real dimension problem is NPIR-complete. To appear in Journal of Complexity, 1997.
    • (1997) Journal of Complexity
    • Koiran, P.1
  • 16
    • 0000238829 scopus 로고
    • Methods of computing values of polynomials
    • V.Y. Pan. Methods of computing values of polynomials. Russian Math. Surveys, 21:105-136, 1966.
    • (1966) Russian Math. Surveys , vol.21 , pp. 105-136
    • Pan, V.Y.1
  • 17
    • 85025505234 scopus 로고
    • On the computational complexity and geometry of the first-order theory of the reals
    • J. Renegar. On the computational complexity and geometry of the first-order theory of the reals. Part I Journal of Symbolic Computation, 13:255-299, 1992.
    • (1992) Part I Journal of Symbolic Computation , vol.13 , pp. 255-299
    • Renegar, J.1
  • 18
    • 0028426653 scopus 로고
    • Some perturbation theory for linear programming
    • J. Renegar. Some perturbation theory for linear programming. Mathematical Programming, 65:73-91, 1994.
    • (1994) Mathematical Programming , vol.65 , pp. 73-91
    • Renegar, J.1
  • 19
    • 0000208672 scopus 로고
    • Incorporating condition measures into the complexity theory of linear programming
    • J. Renegar. Incorporating condition measures into the complexity theory of linear programming. SIAM Journal of Optimization, 5:506-524, 1995.
    • (1995) SIAM Journal of Optimization , vol.5 , pp. 506-524
    • Renegar, J.1
  • 20
    • 0029195774 scopus 로고
    • Linear programming, complexity theory and elementary functional analysis
    • J. Renegar. Linear programming, complexity theory and elementary functional analysis. Mathematical Programming, 70:279-351, 1995.
    • (1995) Mathematical Programming , vol.70 , pp. 279-351
    • Renegar, J.1
  • 21
    • 84968505377 scopus 로고
    • Complexity of bezout's theorem i: Geometric aspects
    • M. Shub and S. Smale. Complexity of Bezout's theorem I: geometric aspects. Journal of the Amer. Math. Soc., 6:459-501, 1993.
    • (1993) Journal of the Amer. Math. Soc. , vol.6 , pp. 459-501
    • Shub, M.1    Smale, S.2
  • 22
    • 0000537756 scopus 로고
    • Complexity of bezout's theorem ii: Volumes and probabilities
    • F. Eyssette and A. Galligo, editors, volume 109 of Progress in Mathematics, Birkhauser
    • M. Shub and S. Smale. Complexity of Bezout's theorem II: volumes and probabilities. In F. Eyssette and A. Galligo, editors, Computational Algebraic Geometry, volume 109 of Progress in Mathematics, pages 267-285. Birkhauser, 1993.
    • (1993) Computational Algebraic Geometry , pp. 267-285
    • Shub, M.1    Smale, S.2
  • 23
    • 0002102930 scopus 로고
    • Complexity of bezout's theorem iii: Condition number and packing
    • M. Shub and S. Smale. Complexity of Bezout's theorem III: condition number and packing. Journal of Complexity, 9:4-14, 1993.
    • (1993) Journal of Complexity , vol.9 , pp. 4-14
    • Shub, M.1    Smale, S.2
  • 24
    • 0028516294 scopus 로고
    • Complexity of bezout's theorem v: Polynomial time
    • M. Shub and S. Smale. Complexity of Bezout's theorem V: polynomial time. Theoretical Computer Science, 133:141-164, 1994.
    • (1994) Theoretical Computer Science , vol.133 , pp. 141-164
    • Shub, M.1    Smale, S.2
  • 25
    • 0000675799 scopus 로고    scopus 로고
    • Complexity of bezout's theorem iv: Probability of success; extensions
    • M. Shub and S. Smale. Complexity of Bezout's theorem IV: probability of success; extensions. SIAM J. of Numer. Anal., 33:128-148, 1996.
    • (1996) SIAM J. of Numer. Anal. , vol.33 , pp. 128-148
    • Shub, M.1    Smale, S.2
  • 26
    • 84966209344 scopus 로고
    • The fundamental theorem of algebra and complexity theory
    • S. Smale. The fundamental theorem of algebra and complexity theory. Bulletin of the Amer. Math. Soc., 4:1-36, 1981.
    • (1981) Bulletin of the Amer. Math. Soc. , vol.4 , pp. 1-36
    • Smale, S.1
  • 27
    • 0025442789 scopus 로고
    • Some remarks on the foundations of numerical analysis
    • S. Smale. Some remarks on the foundations of numerical analysis. SIAM Review, 32:211-220, 1990.
    • (1990) SIAM Review , vol.32 , pp. 211-220
    • Smale, S.1
  • 28
    • 85011523909 scopus 로고    scopus 로고
    • Complexity theory and numerical analysis
    • A. Iserles, editor, Cambridge University Press
    • S. Smale. Complexity theory and numerical analysis. In A. Iserles, editor, Acta Numerica, pages 523-551. Cambridge University Press, 1997.
    • (1997) Acta Numerica , pp. 523-551
    • Smale, S.1
  • 31
    • 38249020377 scopus 로고
    • A note on a theorem of blum, shub, and smale
    • E. Triesch. A note on a theorem of Blum, Shub, and Smale. Journal of Complexity, 6:166-169, 1990.
    • (1990) Journal of Complexity , vol.6 , pp. 166-169
    • Triesch, E.1
  • 32
    • 0000612851 scopus 로고
    • Rounding-off errors in matrix processes
    • A.M. Turing. Rounding-off errors in matrix processes. Quart. J. Mech. Appl. Math., 1:287-308, 1948.
    • (1948) Quart. J. Mech. Appl. Math. , vol.1 , pp. 287-308
    • Turing, A.M.1
  • 35
    • 0001167652 scopus 로고
    • Modern error analyis
    • J. Wilkinson. Modern error analyis. SIAM Review, 13:548-568, 1971.
    • (1971) SIAM Review , vol.13 , pp. 548-568
    • Wilkinson, J.1
  • 36
    • 0001693342 scopus 로고
    • Numerical stability for solving non-linear equations
    • H. Wozniakowski. Numerical stability for solving non-linear equations. Numer. Math., 27:373-390, 1977.
    • (1977) Numer. Math , vol.27 , pp. 373-390
    • Wozniakowski, H.1


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