Information-based complexity (IBC) studies optimal
algorithms
In mathematics and computer science, an algorithm () is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for per ...
and
computational complexity
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations ...
for the continuous problems that arise in
physical science
Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together is called the "physical sciences".
Definition
...
,
economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
,
engineering
Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...
, and
mathematical finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field.
In general, there exist two separate branches of finance that req ...
.
Further reading
*Traub, J. F., Iterative Methods for the Solution of Equations, Prentice Hall, 1964. Reissued Chelsea Publishing Company, 1982; Russian translation MIR, 1985; Reissued American Mathematical Society, 1998
*Traub, J. F., and Woźniakowski, H., A General Theory of Optimal Algorithms, Academic Press, New York, 1980
*Traub, J. F., Woźniakowski, H., and Wasilkowski, G. W., Information, Uncertainty, Complexity, Addison-Wesley, New York, 1983
*Novak, E., Deterministic and Stochastic Error Bounds in Numerical Analysis, Lecture Notes in Mathematics, vol. 1349, Springer-Verlag, New York, 1988
*
*Werschulz, A. G., The Computational Complexity of Differential and Integral Equations: An Information-Based Approach, Oxford University Press, New York, 1991
*Kowalski, M., Sikorski, K., and Stenger, F., Selected Topics in Approximation and Computation, Oxford University Press, Oxford, UK, 1995
*Plaskota, L., Noisy Information and Computational Complexity, Cambridge University Press, Cambridge, UK, 1996
*Traub, J. F., and Werschulz, A. G., Complexity and Information, Oxford University Press, Oxford, UK, 1998
*Ritter, K., Average-Case Analysis of Numerical Problems, Springer-Verlag, New York, 2000
*Sikorski, K., Optimal Solution of Nonlinear Equations, Oxford University Press, Oxford, UK, 2001
Extensive bibliographies may be found in the monographs N (1988), TW (1980), TWW (1988) and TW (1998).
Th
IBC websitehas a searchable data base of some 730 items.
External links
Journal of ComplexityComplexity and InformationJoseph TraubJ.F Traub, 1985. An Introduction to Information-Based Complexity
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Computational complexity theory