Complexity lower bounds for approximation algebraic computation trees

Journal of Complexity

Volumn 15, Issue 4, 1999, Pages 499-512

  Cucker, Felipe ^a   Grigoriev, Dima ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346728832     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.1999.0519     Document Type: Article

References (14)

1. Blum L., Cucker F., Shub M., Smale S. Complexity and Real Computation. 1998;Springer-Verlag, New York/Berlin.
2. Bürgisser P., Clausen M., Shokrollahi A. Algebraic Complexity Theory. 1996;Springer-Verlag, New York/Berlin.
3. Cucker F., Smale S. Complexity estimates depending on condition and round-off error. Assoc. Comput. Mach. 46:1999;113-184.
4. Demmel J. Applied Numerical Linear Algebra. 1997;SIAM, Philadelphia.
5. Grigoriev D. Nearly sharp complexity bounds for multiprocessor algebraic computations. J. Complexity. 13:1997;50-64.
6. D. Grigoriev, Randomized complexity lower bounds, in 30th Annual ACM Symp. on the Theory of Computing, 1998, pp. 219-223.
7. D. Grigoriev, M. Karpinski, and, A. Yao, An exponential lower bound on the size of algebraic decision trees for MAX problem, Comput. Complexity, in press.
8. P. Koiran, Approximating the volume of definable sets, in 36th Annual IEEE Symp. on Foundations of Computer Science, 1995, pp. 134-141.
9. Montaña J., Pardo L. Lower bounds for arithmetic networks. Appl. Algebra Eng. Comm. Comput. 4:1993;1-24.
10. Renegar J. On the worst case arithmetic complexity of approximating zeros of polynomials. J. Complexity. 3:1987;90-113.
11. Smale S. On the topology of algorithms, I. J. Complexity. 3:1987;81-89.
12. Strassen V. The computational complexity of continued fractions. SIAM J. Comput. 12:1983;1-27.
13. Vassiliev V. Complements of Discriminants of Smooth Maps: Topology and Applications. Translations of Mathematical Monographs. 98:1992;Amer. Math. Soc. Providence.
14. A. Yao, On the parallel computation of the knapsack problem, in 13th Annual ACM Symp. on the Theory of Computing, 1981, pp. 123-127.