A Simple Recipe for Modelling a d − cube by Lissajous curves

  title={A Simple Recipe for Modelling a d − cube by Lissajous curves},
  author={Len Bos},
We give a simple recipe for Lissajous curves that for (certain) numerical purposes can serve as a proxy for the cube [−1, 1]d . For a ∈ Zd >0 we let `a(t) := (cos(a1 t), cos(a2 t), · · · , cos(ad t)), t ∈ R. (1) denote the associated Lissajous curve with frequencies a1, · · · , ad . We note that such curves are given by the fundamental parameter interval t ∈ [0,π]. The recent articles [2] and [3] discuss the use of such Lissajous curves as a proxy for the cube [−1,1]d , for the purposes of… CONTINUE READING


Publications referenced by this paper.
Showing 1-5 of 5 references

Polynomial approximation on Lissajous curves in the d-cube

L. Bos, S. De Marchi, M. Vianello
Appl. Numer. Math., published online January • 2017
View 4 Excerpts
Highly Influenced

Metrics Associated to Multivariate Polynomial Inequalities, in Advances in Constructive Approximation

L. Bos, N. Levenberg, S. Waldron
View 1 Excerpt

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