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Abstract: We study the worst case complexity of computing #-approximations of surface integrals. This problem has two sources of partial information: the integrand f and the function g defining the surface. The problem is nonlinear in its dependence on g. Here, f is an r times continuously differentiable scalar function of l variables, and g is an s times continuously differentiable injective function of d variables with l components. We must have d # l and s # 1 for surface integration to be... (Update)
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...when d = 1, we concentrate our attention on the case d # 2. This problem is a special case of the surface integration problem studied in [12]. Let c be the cost of one function evaluation. The results of [12] might suggest that the # complexity of volume calculation should...
...a class of such functions g. The simplest situation is to let # g ) where G is a class of functions from I to I , as was studied in [11] and [12] Note that such a domain # g is the diffeomorphic image of a cube, and hence # g must have corners. If we want to allow smooth...
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What is the Complexity of Volume Calculation? - Werschulz, Wozniakowski (2000) (Correct)
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2: Direct Methods in the Calculus of Variations (context) - Dacorogna - 1989
2: The Finite Element Method for Elliptic Problems (context) - Ciarlet - 1978
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BibTeX entry: (Update)
A. G. Werschulz and H. Wozniakowski. What is the complexity of surface integration? Journal of Complexity, 2001. (to appear). 18 http://citeseer.ist.psu.edu/werschulz01what.html More
@article{ werschulz01what,
author = "Werschulz and Wozniakowski",
title = "What Is the Complexity of Surface Integration?",
journal = "COMPLEXITY: Journal of Complexity",
volume = "17",
year = "2001",
url = "citeseer.ist.psu.edu/werschulz01what.html" }
Citations (may not include all citations):689 The Finite Element Method For Elliptic Problems (context) - Ciarlet - 1978
179 Spline Functions: Basic Theory (context) - --, Schumaker - 1981
134 Information-Based Complexity (context) - Traub, Wasilkowski et al. - 1988
42 Deterministic and Stochastic Error Bounds in Numerical Analy.. (context) - Novak - 1988
27 A General Theory of Optimal Algorithms (context) - Traub, Wozniakowski - 1980
27 Complexity and Information (context) - Traub, Werschulz - 1998
20 The Computational Complexity of Differential and Integral Eq.. (context) - Werschulz - 1991
17 Green's Functions and Boundary Value Problems (context) - Stakgold - 1998
16 On approximate calculation of integrals (context) - Bakhvalov - 1959
13 Approximation of functions with bounded mixed derivatives (context) - Temlyakov - 1989
12 Advanced Calculus of Several Variables (context) - Edwards - 1973
11 When are quasi-Monte Carlo algorithms efficient for high dim.. - Sloan, Wozniakowski - 1998
2 multivariate approximation theory (context) - Schultz - 1969
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