Asymptotically optimal designs on compact algebraic manifolds. (English) Zbl 1479.05040
Summary: We find \(t\)-designs on compact algebraic manifolds with a number of points comparable to the dimension of the space of polynomials of degree \(t\) on the manifold. This generalizes results on the sphere by A. Bondarenko et al. [Ann. Math. (2) 178, No. 2, 443–452 (2013; Zbl 1270.05026)]. Of special interest is the particular case of the Grassmannians where our results improve the bounds that had been proved previously.
MSC:
| 05B30 | Other designs, configurations |
| 41A55 | Approximate quadratures |
| 41A63 | Multidimensional problems |
| 52C35 | Arrangements of points, flats, hyperplanes (aspects of discrete geometry) |
| 65D30 | Numerical integration |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
Citations:
Zbl 1270.05026References:
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