Preprint Series 2010
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2010:01
E. Liu and
V. Temlyakov
The general theory of greedy approximation is well developed. Much less is known about how specific features of a dictionary can be used for our advantage. In this paper we discuss incoherent dictionaries. We build a new greedy algorithm which is called the Orthogonal Super Greedy Algorithm (OSGA). OSGA is ...
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2010:02
V. Temlyakov and
P. Zheltov
In this paper we show that for dictionaries with small coherence in a Hilbert space the Orthogonal Greedy Algorithm (OGA) performs almost as well as the best m-term approximation for all signals with sparsity almost as high as the best theoretically possible threshold $s = 1/2 (M^{-1} + 1)$ by ...
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2010:03
P. Binev,
W. Dahmen, and
P. Lamby
This paper is concerned with scattered data approximation in high dimensions: Given a data set X in R^d of N data points x^i along with values y^i in R^{d'}, i = 1, ..., N, and viewing the yi as values y_i = f(x_i) of some unknown function f ...
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2010:04
G. Kyriazis and
P. Petrushev
Frames are constructed on the unit ball Bd in ℜd consisting of smooth functions with small shrinking supports. The new frames are designed so that they can be used for decomposition of weighted Triebel Lizorkin and Besov spaces on Bd with weight ωμ(χ):= (1 - │χ ...
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2010:05
P. Binev,
A. Cohen,
W. Dahmen,
R. DeVore,
G. Petrova, and
P. Wojtaszczyk
The reduced basis method was introduced for the accurate online evaluation of solutions to a parameter dependent family of elliptic partial differential equations. Abstractly, it can be viewed as determining a “good” n dimensional space H_n to be used in approximating the elements of a compact set F in a ...
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2010:06
D. Bilyk,
V. Temlyakov, and
R. Yu
We study the Fibonacci sets from the point of view of their quality for numerical integration and discrepancy. Let
[Full Abstract]{b_n}_{n=0}^{\infty}be the sequence of Fibonacci numbers. The b_nn-point Fibonacci setF_n\in [0,1]^2is defined asF_n := f{(\mu/b_n; {\mub_{n-1})}_\mu ... -
2010:07
E. Liu and
V. Temlyakov
We study greedy-type algorithms such that at a greedy step we pick several dictionary elements contrary to a single dictionary element in standard greedy-type algorithms. We call such greedy algorithms super greedy algorithms. The idea of picking several elements at a greedy step of the algorithm is not new. Recently ...
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2010:08
A. Belochitski,
P. Binev,
R. DeVore,
M. Fox-Rabinovitz,
V. Krasnopolsky, and
P. Lamby
The computation of Global Climate Models (GCMs) presents significant numerical challenges. This paper presents new algorithms based on sparse occupancy trees for learning and emulating the long wave radiation parameterization in the NCAR CAM climate model. This emulation occupies by far the most significant portion of the computational time in ...
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2010:09
P. Binev,
W. Dahmen,
R. DeVore,
P. Lamby,
D. Savu, and
R. Sharpley
Compressed Sensing (CS) is a relatively new approach to signal acquisition which has as its goal to minimize the number of measurements needed of the signal in order to guarantee that it is captured to a prescribed accuracy. It is natural to inquire whether this new subject has a role ...
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2010:10
P. Binev,
F. Blanco-Silva,
D. Blom,
W. Dahmen,
P. Lamby,
R. Sharpley, and
T. Vogt
We outline a new systematic approach to extracting high quality information from HAADF-STEM images which will be beneficial to the characterization of beam sensitive materials. The idea is to treat several, possibly many low electron dose images with specially adapted digital image processing concepts at a minimum allowable spatial resolution ...
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