Owing to the natural interpretation and various desirable mathematical properties, centroidal Voronoi tessellations (CVTs) have found a wide range of applications correspondingly vast development in their literature. However, computation CVTs higher dimensional spaces remains difficult. In this paper, we exploit non-uniqueness for computation. We construct such high by decomposing into one-dime...

We prove that the spectral structure on $N$-dimensional standard sphere of radius $(N - 1)^{1/2}$ compatible with a projection onto first $n$-coordinates converges to $n$-dimensional Gaussian space variance 1 as $N \rightarrow \infty$. also show analogue for Dirichlet eigenvalue problem ball in and halfspace space.

We study computation of the mean of sequences with values in finite dimensional normed spaces and compare the computational power of classical randomized with that of quantum algorithms for this problem. It turns out that in contrast to the known superiority of quantum algorithms in the scalar case, in high dimensional LMp spaces classical randomized algorithms are essentially as powerful as qu...