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Analysis of Framelet Transforms on a Simplex

In: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Author

Listed:
  • Yu Guang Wang

    (La Trobe University, Department of Mathematics and Statistics)

  • Houying Zhu

    (The University of Melbourne, School of Mathematics and Statistics)

Abstract

In this paper, we construct framelets associated with a sequence of quadrature rules on the simplex T 2 in ℝ 2 $$\mathbb {R}^{2}$$ . We give the framelet transforms—decomposition and reconstruction of the coefficients for framelets of a function on T 2. We prove that the reconstruction is exact when the framelets are tight. We give an example of construction of framelets and show that the framelet transforms can be computed as fast as FFT.

Suggested Citation

  • Yu Guang Wang & Houying Zhu, 2018. "Analysis of Framelet Transforms on a Simplex," Springer Books, in: Josef Dick & Frances Y. Kuo & Henryk Woźniakowski (ed.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pages 1175-1189, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-72456-0_54
    DOI: 10.1007/978-3-319-72456-0_54
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