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ALGORITHMICA
2008
78views more  ALGORITHMICA 2008»
13 years 5 months ago
Optimally Adaptive Integration of Univariate Lipschitz Functions
We consider the problem of approximately integrating a Lipschitz function f (with a known Lipschitz constant) over an interval. The goal is to achieve an error of at most using as...
Ilya Baran, Erik D. Demaine, Dmitriy A. Katz
DAGSTUHL
2004
13 years 6 months ago
Optimal algorithms for global optimization in case of unknown Lipschitz constant
We consider the global optimization problem for d-variate Lipschitz functions which, in a certain sense, do not increase too slowly in a neighborhood of the global minimizer(s). O...
Matthias U. Horn
JUCS
2008
151views more  JUCS 2008»
13 years 4 months ago
The Bit-Complexity of Finding Nearly Optimal Quadrature Rules for Weighted Integration
: Given a probability measure and a positive integer n. How to choose n knots and n weights such that the corresponding quadrature rule has the minimum worst-case error when appli...
Volker Bosserhoff
CORR
2011
Springer
158views Education» more  CORR 2011»
12 years 12 months ago
SqFreeEVAL: An (almost) optimal real-root isolation algorithm
Let f be a univariate polynomial with real coefficients, f ∈ R[X]. Subdivision algorithms based on algebraic techniques (e.g., Sturm or Descartes methods) are widely used for is...
Michael Burr, Felix Krahmer
COLT
2008
Springer
13 years 6 months ago
Adaptive Hausdorff Estimation of Density Level Sets
Consider the problem of estimating the -level set G = {x : f(x) } of an unknown d-dimensional density function f based on n independent observations X1, . . . , Xn from the densi...
Aarti Singh, Robert Nowak, Clayton Scott