اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDispersion of the Fibonacci and the Frolov point sets
111
0
0.0
(
0
)
تأليف
V.N. Temlyakov
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
It is proved that the Fibonacci and the Frolov point sets, which are known to be very good for numerical integration, have optimal rate of decay of dispersion with respect to the cardinality of sets. This implies that the Fibonacci and the Frolov point sets provide universal discretization of the uniform norm for natural collections of subspaces of the multivariate trigonometric polynomials. It is shown how the optimal upper bounds for dispersion can be derived from the upper bounds for a new characteristic -- the smooth fixed volume discrepancy. It is proved that the Fibonacci point sets provide the universal discretization of all integral norms.
قيم البحث
اقرأ أيضاً
This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Korobov point sets in the unit cube. It was observed recently that this new characteristic allows us to obtain optimal rate of dispersio
n from numerical integration results. This observation motivates us to thoroughly study this new version of discrepancy, which seems to be interesting by itself. This paper extends recent results by V. Temlyakov and M. Ullrich on the fixed volume discrepancy of the Fibonacci point sets.
For a positive integer $d$, the $d$-dimensional Chebyshev-Frolov lattice is the $mathbb{Z}$-lattice in $mathbb{R}^d$ generated by the Vandermonde matrix associated to the roots of the $d$-dimensional Chebyshev polynomial. It is important to enumerate
the points from the Chebyshev-Frolov lattices in axis-parallel boxes when $d = 2^n$ for a non-negative integer $n$, since the points are used for the nodes of Frolovs cubature formula, which achieves the optimal rate of convergence for many spaces of functions with bounded mixed derivatives and compact support. The existing enumeration algorithm for such points by Kacwin, Oettershagen and Ullrich is efficient up to dimension $d=16$. In this paper we suggest a new enumeration algorithm of such points for $d=2^n$, efficient up to $d=32$.
In this paper, we give the Minc-type bound for spectral radius of nonnegative tensors. We also present the bounds for the spectral radius and the eigenvalue inclusion sets of the general product of tensors.
We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. For the latter, we present a new abstract analysis, based on weaker assumptions on the stabilization, and numerical results on the disper
sion analysis, including comparison with the plane wave discontinuous Galerkin method.
Geometrical objects with integral sides have attracted mathematicians for ages. For example, the problem to prove or to disprove the existence of a perfect box, that is, a rectangular parallelepiped with all edges, face diagonals and space diagonals
of integer lengths, remains open. More generally an integral point set $mathcal{P}$ is a set of $n$ points in the $m$-dimensional Euclidean space $mathbb{E}^m$ with pairwise integral distances where the largest occurring distance is called its diameter. From the combinatorial point of view there is a natural interest in the determination of the smallest possible diameter $d(m,n)$ for given parameters $m$ and $n$. We give some new upper bounds for the minimum diameter $d(m,n)$ and some exact values.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
