Spherical designs of harmonic index t
نویسندگان
چکیده
منابع مشابه
On Spherical Designs of Some Harmonic Indices
A finite subset Y on the unit sphere Sn−1 ⊆ Rn is called a spherical design of harmonic index t, if the following condition is satisfied: ∑ x∈Y f(x) = 0 for all real homogeneous harmonic polynomials f(x1, . . . , xn) of degree t. Also, for a subset T of N = {1, 2, · · · }, a finite subset Y ⊆ Sn−1 is called a spherical design of harmonic index T, if ∑ x∈Y f(x) = 0 is satisfied for all real homo...
متن کاملComputational existence proofs for spherical t-designs
Spherical t-designs provide quadrature rules for the sphere which are exact for polynomials up to degree t. In this paper, we propose a computational algorithm based on interval arithmetic which, for given t, upon successful completion will have proved the existence of a tdesign with (t + 1)2 nodes and will have computed narrow interval enclosures which are known to contain these nodes with mat...
متن کاملRobust Designs for 3d Shape Analysis with Spherical Harmonic Descriptors
Spherical harmonic descriptors are frequently used for describing threedimensional shapes in terms of Fourier coefficients corresponding to an expansion of a function defined on the unit sphere. In a recent paper Dette, Melas and Pepelysheff (2005) determined optimal designs with respect to Kiefer’s Φp-criteria for regression models derived from a truncated Fourier series. In particular it was ...
متن کاملNew spherical 4-designs
Hardin, R.H. and N.J.A. Sloane, New spherical 4-designs, Discrete Mathematics 106/107 (1992) 255-264. This paper gives a number of new spherical 4-designs, and presents numerical evidence that spherical 4-designs containing n points in k-dimensional space with k G 8 exist precisely for the following values of n and k: n even and 22 for k = 1; n 2 5 for k = 2; n = 12, 14, >I6 for k=3;n~2Ofork=4;...
متن کاملOn Tight Spherical Designs
Let X be a tight t-design of dimension n for one of the open cases t = 5 or t = 7. An investigation of the lattice generated by X using arithmetic theory of quadratic forms allows to exclude infinitely many values for n.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2015
ISSN: 0021-9045
DOI: 10.1016/j.jat.2014.06.010