A sequentially optimal algorithm for numerical integration |
| |
Authors: | A G Sukharev |
| |
Institution: | (1) Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, USSR;(2) Present address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, California |
| |
Abstract: | For the class of functions of one variable, satisfying the Lipschitz condition with a fixed constant, an optimal passive algorithm for numerical integration (an optimal quadrature formula) has been found by Nikol'skii. In this paper, a sequentially optimal algorithm is constructed; i.e., the algorithm on each step makes use in an optimal way of all relevant information which was accumulated on previous steps. Using the algorithm, it is necessary to solve an integer program at each step. An effective algorithm for solving these problems is given.The author is indebted to Professor S. E. Dreyfus, Department of Industrial Engineering and Operations Research, University of California, Berkeley, California, for his helpful attention to this paper. |
| |
Keywords: | Numerical integration quadrature formulas worst-case algorithms minimax problems |
本文献已被 SpringerLink 等数据库收录! |
|