This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.L. Allgower and K. Georg. Numerical Continuation Methods. Springer-Verlag, 1990.
J.L. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I. EATCS Monographs on Theoretical Computer Science, 11. Springer-Verlag, 1988.
S. Basu, R. Pollack, and M.-F. Roy. On the combinatorial and algebraic complexity of quantifier elimination. In 35th annual IEEE Symp. on Foundations of Computer Science, pages 632–641, 1994.
L. Blum, F. Cucker, M. Shub, and S. Smale. Complexity and Real Computation. Springer-Verlag, 1998.
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.
S.L. Campbell and C.D. Meyer. Generalized Inverses of Linear Transformations. Pitman, 1979.
G.E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic deccomposition, volume 33 of Lect. Notes in Comp. Sci., pages 134–183. Springer-Verlag, 1975.
F. Cucker and S. Smale. Complexity estimates depending on condition and round-off error. Preprint, 1997.
J.-P. Dedieu and M. Shub. Multihomogeneous Newton methods. Preprint, 1997.
D.Yu. Grigoriev and N.N. Vorobjov. Solving systems of polynomial inequalities in subexponential time. Journal of Symbolic Computation, 5:37–64, 1988.
J. Heintz, M.-F. Roy, and P. Solerno. Sur la complexité du principe de Tarski-Seidenberg. Bulletin de la Société Mathématique de France, 118:101–126, 1990.
N. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, 1996.
C.H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.
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.
M. Shub and S. Smale. Complexity of Bezout’s theorem I: geometric aspects. Journal of the Amer. Math. Soc., 6:459–501, 1993.
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. Birkhäuser, 1993.
M. Shub and S. Smale. Complexity of Bezout’s theorem III: condition number and packing. Journal of Complexity, 9:4–14, 1993.
M. Shub and S. Smale. Complexity of Bezout’s theorem V: polynomial time. Theoretical Computer Science, 133:141–164, 1994.
M. Shub and S. Smale. Complexity of Bezout’s theorem IV: probability of success; extensions. SIAM J. of Numer. Anal., 33:128–148, 1996.
S. Smale. Complexity theory and numerical analysis. In A. Iserles, editor, Acta Numerica, pages 523–551. Cambridge University Press, 1997.
A. Tarski. A Decision Method for Elementary Algebra and Geometry. University of California Press, 1951.
L.N. Trefethen and D. Bau III. Numerical Linear Algebra. SIAM, 1997.
J. Wilkinson. Rounding Errors in Algebraic Processes. Prentice Hall, 1963.
J. Wilkinson. Modern error analyis. SIAM Review, 13:548–568, 1971.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cucker, F., Smale, S. (1998). Complexity Estimates Depending on Condition and Round-Off Error. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_10
Download citation
DOI: https://doi.org/10.1007/3-540-68530-8_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64848-2
Online ISBN: 978-3-540-68530-2
eBook Packages: Springer Book Archive