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Fast Computation of Polynomial Data Points Over Simplicial Face Values

Author

Listed:
  • Tareq Hamadneh

    (Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, Jordan)

  • Hassan Al-Zoubi

    (Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, Jordan)

  • Saleh Ali Alomari

    (#x2020;Faculty of Science and Information Technology, Jadara University, Irbid, Jordan)

Abstract

Polynomial functions F of degree m have a form in the Bernstein basis defined over l-dimensional simplex W. The Bernstein coefficients exhibit a number of special properties. The function F can be optimised by the smallest and largest Bernstein coefficients (enclosure bounds) over W. By a proper choice of barycentric subdivision steps of W, we prove the inclusion property of Bernstein enclosure bounds. To this end, we provide an algorithm that computes the Bernstein coefficients over subsimplices. These coefficients are collected in an l-dimensional array in the field of computer-aided geometric design. Such a construct is typically classified as a patch. We show that the Bernstein coefficients of F over the faces of a simplex coincide with the coefficients contained in the patch.

Suggested Citation

  • Tareq Hamadneh & Hassan Al-Zoubi & Saleh Ali Alomari, 2020. "Fast Computation of Polynomial Data Points Over Simplicial Face Values," Journal of Information & Knowledge Management (JIKM), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-13, March.
    • Handle: RePEc:wsi:jikmxx:v:19:y:2020:i:01:n:s0219649220400018
    DOI: 10.1142/S0219649220400018
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    References listed on IDEAS

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    1. de Klerk, E. & den Hertog, D. & Elabwabi, G., 2008. "On the complexity of optimization over the standard simplex," European Journal of Operational Research, Elsevier, vol. 191(3), pages 773-785, December.
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