Optimal cubature formulas related to tomography for certain classes of functions defined on a cube

Vladyslav Babenko ^[1] ; Sergiy Borodachov ^[2] ; Dmytro Skorokhodov ^[1]
1. [1] National University
  
  National University
  
  Estados Unidos
2. [2] Towson University
  
  Towson University
  
  Estados Unidos
Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 3, Nº. 2, 2011, págs. 143-160
Idioma: inglés
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Resumen
- We study the problem of constructing an optimal cubature formula for approximate integration over the cube [0, 1]d . Our construction uses the information given by n integrals along intersections of [0, 1]d with shifts of coordinate subspaces of a given codimension k, 0 < k < d. We find a family of optimal formulas of this type for the class of functions defined on [0, 1]d which controls the modulus of continuity with respect to the max-norm in R d . When the majorant ω for the moduli of continuity of functions in the class is strictly increasing the family we find describes the set of all optimal cubature formulas.