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ALGORITHMICA
2008
78views more  ALGORITHMICA 2008»
13 years 9 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 11 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 9 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»
13 years 4 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 11 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