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Construction of Optimal Cubature Formulas Related to Computer Tomography

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Constructive Approximation Aims and scope

Abstract

We study the problem of the optimization of approximate integration on the class of functions defined on the parallelepiped Π d =[0,a 1]×⋅⋅⋅×[0,a d ], a 1,…,a d >0, having a given majorant for the modulus of continuity (relative to the l 1-metric in ℝd). An optimal cubature formula, which uses as information integrals of f along intersections of Π d with n arbitrary (d−1)-dimensional hyperplanes in ℝd (d>1) is obtained. We also find an asymptotically optimal sequence of cubature formulas, whose information functionals are integrals of f along intersections of Π d with shifts of (d−2)-dimensional coordinate subspaces of ℝd (d>2).

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Authors and Affiliations

  1. Dnepropetrovsk National University, Dnepropetrovsk, 49050, Ukraine

    V. F. Babenko & D. S. Skorokhodov

  2. Institute of Applied Mathematics and Mechanics of NAS, Donetsk, 83114, Ukraine

    V. F. Babenko

  3. Towson University, Baltimore, MD, 21252, USA

    S. V. Borodachov

Authors
  1. V. F. Babenko
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  2. S. V. Borodachov
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  3. D. S. Skorokhodov
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Correspondence to S. V. Borodachov.

Additional information

Communicated by Tim N.T. Goodman.

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Babenko, V.F., Borodachov, S.V. & Skorokhodov, D.S. Construction of Optimal Cubature Formulas Related to Computer Tomography. Constr Approx 33, 313–330 (2011). https://doi.org/10.1007/s00365-010-9095-6

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  • DOI: https://doi.org/10.1007/s00365-010-9095-6

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