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 few samples of f as possible. We use the adaptive framework: on all problem instances an adaptive algorithm should perform almost as well as the best possible algorithm tuned for the particular problem instance. We distinguish between DOPT and ROPT, the performances of the best possible deterministic and randomized algorithms, respectively. We give a deterministic algorithm that uses O(DOPT(f, )

• Type: Journal
• Year: 2008
• Where: ALGORITHMICA
• Authors: Ilya Baran, Erik D. Demaine, Dmitriy A. Katz
• Keywords: Adaptive Algorithm, Algorithm, ALGORITHMICA 2008, Problem Instance