Preprint Series 2015

2015:07
P. Binev
The hpadaptive approximation is formulated as an approximation problem on a full binary tree $T$, where for each of the leaves $\Delta$ an order $p(\Delta)\ge1$ is assigned in such a way that the sum of all such $p(\Delta)$ does not exceed $N$, called complexity of the approximation ...
[Full Abstract] 
2015:06
G. Kerkyacharian,
S. Ogawa,
P. Petrushev, and
D. Picard
We are interested in the regularity of centered Gaussian processes $(Z _ x( \omega )) _ {x\in M}$ indexed by compact metric spaces $(M, \rho)$. It is shown that the almost everywhere Besov space regularity of such a process is (almost) equivalent to the Besov regularity of the covariance $K ...
[Full Abstract] 
2015:05
J. Griggs and
W. Li
Increasing attention is being paid to the study of families of subsets of an $n$set that contain no subposet $P$. Especially, we are interested in such families of maximum size given $P$ and $n$. For certain $P$ this problem is solved for general $n$, while for other $P$ it ...
[Full Abstract] 
2015:04
J. Griggs and
W. Li
Given a finite poset $P$, we consider the largest size $\mathrm{La}(n,P)$ of a family $\mathcal{F}$ of subsets of $[n]:=\{1,\ldots,n\}$ that contains no subposet $P$. This continues the study of the asymptotic growth of $\mathrm{La}(n,P)$; it has been conjectured that for ...
[Full Abstract] 
2015:03
M. Lind and
P. Petrushev
Nonlinear approximation from regular piecewise polynomials (splines) supported on rings in $\mathbb{R}^2$ is studied. By definition a ring is a set in $\mathbb{R}^2$ obtained by subtracting a compact convex set with polygonal boundary from another such a set, but without creating uncontrollably narrow elongated subregions. Nested ...
[Full Abstract] 
2015:02
T. Sanders
Discrete tomography refers to tomographic reconstruction of images that are known to contain only a few intensity levels. We propose a new reconstruction technique for discrete tomography that uses a relaxed partial segmentation and a refinement update in each iteration. With our approach the dimension of the tomographic reconstruction problem ...
[Full Abstract] 
2015:01
K. Ivanov and
P. Petrushev
An algorithm for fast and accurate evaluation of bandlimited functions at many scattered points on the unit 2d sphere is developed. The algorithm is based on trigonometric representation of spherical harmonics in spherical coordinates and highly localized tensorproduct trigonometric kernels (needlets). It is simple, fast, local, memory efficient, numerically stable ...
[Full Abstract]