Conjecture on monotonicity of worst-case error for spherical t-designs
Conjecture on monotonicity of worst-case error for spherical t-designs
Let denote the quadrature rule associated with a spherical -design consisting of points, and let be its worst-case error.
Worst-case error monotonicity conjecture. For fixed , if , then
The conjecture is motivated by numerical experiments comparing well-conditioned and efficient spherical -designs. It predicts that increasing the number of points does not increase the worst-case error, but the source provides no proof or resolution.
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Sources & referencesView supporting material
Primary source
Congpei An and Siyong Chen, “Numerical Integration over the Unit Sphere by using spherical t-design”, arXiv:1611.02785 (2016).
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