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Book Review

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Book Information

Author(s): J. F. Traub and A. G. Werschulz
Title: Complexity and information
Additional book information: Cambridge University Press, Cambridge, 1998, xii + 139 pp., $19.95, ISBN 0-521-48506-1 (paperback)

References:

[BSS]
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, Bull. Amer. Math. Soc. 21 (1989), 1-46. MR 90a:68022

[BCSS]
L. Blum, F. Cucker, F. Shub, and S. Smale, Complexity and Real Computation, Springer-Verlag, New York, 1998. MR 99a:68070

[CA]
D. Ceperley and B. Adler, Quantum Monte Carlo, Science 231 (1986), 555-560.

[HS]
M. Hirsch and S. Smale, On algorithms for solving $f(x)=0$, Comm. Pure Appl. Math. 2 (1979), 281-312. MR 80b:65061

[L]
S. Lloyd, Measures of Complexity, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA.

[PW]
E. Packel and H. Wo $\acute{\text{z}}$niakowski, Recent developments in$\,$information-based complexity, Bull. Amer. Math. Soc. 17 (1987), 9-36. MR 88h:65006

[PT]
E. Packel and J. Traub, Information-based complexity,$\,$Nature 327 (1987), 29-33.

[S]
S. Smale, On the efficiency of algorithms of analysis,$\,$Bull. Amer. Math. Soc. 13 (1985), 87-121. MR 86m:65061

[SW]
I. Sloan and H. Wo $\acute{\text{z}}$niakowski, When are quasi-Monte Carlo algorithms efficient for high dimensional integrals? J. Complexity 14 (1998), 1-33. MR 99d:65384

[Tr]
J. Traub, On reality and models, in Boundaries and Barriers: On the Limits to Scientific Knowledge, Addison-Wesley, Reading, 1996, 238-254.

[TW]
J. Traub and H. Wo $\acute{\text{z}}$niakowski, Breaking intractability, Scientific American 270 (1994), 102-107.

[T]
J. Traub, Iterative methods for the solution of equations, Prentice-Hall, Englewood Cliffs, N.J., 1964. MR 29:6607

[TWW]
J. Traub, G. Wasilkowski, and H. Wo $\acute{\text{z}}$niakowski, Information-Based Complexity, Academic Press, Boston, 1988. MR 90f:68085

[W]
A. Werschulz, The Computational Complexity of Differential and Integral Equations: An Information-Based Approach, Oxford University Press, New York, 1991. MR 93a:68061

[Wo]
H. Wo $\acute{\text{z}}$niakowski, Complexity of multivariate problems with applications to path integrals, Z. Angew. Math. Mech. 3 (1996), 131-134.

Additional Information:

Reviewer(s):
Mark A. Kon
Affiliation: Boston University
Email: mkon@math.bu.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 37 (2000), 199-204.

MSC (2000): Primary 65J05, 68Q01; Secondary 68Q05, 68Q15, 68Q25
DOI: 10.1090/S0273-0979-99-00859-9
PII: S 0273-0979(99)00859-9
Posted: December 21, 1999
Copyright of article: Copyright 2000, American Mathematical Society

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