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A sequentially optimal algorithm for numerical integration

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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.

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References

  1. Nikol'skii, S. M.,Concerning Estimation for Approximate Quadrature Formulas (in Russian), Uspehi Matematičeskih Nauk, Vol. 5, No. 2, 1950.

  2. Nikol'skii, S. M.,Quadrature Formulas (in Russian), 2nd Edition, Nauka, Moscow, USSR, 1974.

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  3. Sukharev, A. G.,Optimal Strategies of the Search for an Extremum, USSR Computational Mathematics and Mathematical Physics, Vol. 11, No. 4, 1971.

  4. Sukharev, A. G.,Best Sequential Search Strategies for Finding an Extremum, USSR Computational Mathematics and Mathematical Physics, Vol. 12, No. 1, 1972.

  5. Sukharev, A. G.,Optimal Search for the Roots of a Function Satisfying a Lipschitz Condition, USSR Computational Mathematics and Mathematical Physics, Vol. 16, No. 1, 1976.

  6. Sukharev, A. G.,Optimal Passive and Sequentially Optimal Algorithms for Constructing Best Approximations for Functions Satisfying a Lipschitz Condition, Soviet Mathematics, Doklady, Vol. 17, No. 6, 1976.

  7. Sukharev, A. G.,Optimal Search for an Extremum (in Russian), Moscow State University, Moscow, USSR, 1975.

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  8. Gross, O.,A Class of Discrete Type Minimization Problems, The Rand Corporation, Research Memorandum No. 1644, 1956.

  9. Saaty, T. L.,Optimization in Integers and Related Extremal Problems, McGraw-Hill Book Company, New York, New York, 1970.

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Author notes

  1. A. G. Sukharev (Associate Professor)

    Present address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, California

Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, USSR

    A. G. Sukharev (Associate Professor)

Authors
  1. A. G. Sukharev
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Additional information

Communicated by S. E. Dreyfus

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.

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Sukharev, A.G. A sequentially optimal algorithm for numerical integration. J Optim Theory Appl 28, 363–373 (1979). https://doi.org/10.1007/BF00933380

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  • DOI: https://doi.org/10.1007/BF00933380

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