Constructive Characteristic of ho¨ Lder Classes and M-Term Approximations in the Multiple Haar Basis

2014 ◽  
Vol 66 (3) ◽  
pp. 391-403
Author(s):  
V. S. Romanyuk
Keyword(s):  
Haar Basis ◽  
Constructive Characteristic

scholarly journals On the convergence of greedy algorithms for initial segments of the Haar basis

2010 ◽  
Vol 148 (3) ◽  
pp. 519-529 ◽  
Author(s):  
S. J. DILWORTH ◽  
E. ODELL ◽  
TH. SCHLUMPRECHT ◽  
ANDRÁS ZSÁK
Keyword(s):  
Banach Space ◽  
Greedy Algorithm ◽  
General Result ◽  
Initial Segment ◽  
Greedy Algorithms ◽  
Dimensional Banach Space ◽  
Haar Basis ◽  
Finite Dimensional ◽  
Finite Dimensional Banach Space ◽  
Number Of Iterations

AbstractWe consider the X-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in Lp[0, 1] (1 < p < ∞) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases.

scholarly journals Longlobtorsie bij de hond

2013 ◽  
Vol 82 (3) ◽  
pp. 155-161
Author(s):  
Y. Baeumlin ◽  
V. Bavegems ◽  
H. De Rooster
Keyword(s):  
Haar Basis

Longlobtorsie wordt niet frequent gezien bij honden maar uitstel van diagnose en behandeling leidt tot een levensbedreigende situatie. Door de draaiing van de lob ter hoogte van haar basis, wordt de bloedtoevoer afgesnoerd en de bronchus toegesnoerd. Gepredisponeerde rassen zijn grote hondenrassen met een diepe thorax, zoals de Afghaanse windhond, hoewel ook bij verschillende kleine hondenrassen gevallen worden vastgesteld. Meestal treedt acute ademnood op, hoewel dit niet bij alle gevallen van longlobtorsie gezien wordt. De oorzaak is meestal idiopathisch (spontaan). Secundaire gevallen worden beschreven bij patiënten met pleurale effusie of met een voorgeschiedenis van recente (thorax)chirurgie. De behandeling is altijd chirurgisch en bestaat uit lobectomie van de aangetaste longlob. De prognose na chirurgie wordt beïnvloed door eventuele onderliggende pathologieën. In dit artikel worden het voorkomen, de pathofysiologie, de klinische symptomen, de beeldvormingstechnieken en de chirurgische behandeling van longlobtorsie bij de hond beschreven.

scholarly journals ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS

2018 ◽  
Vol 14 (3) ◽  
pp. 83-102
Author(s):  
Marina L. Mozgaleva ◽  
Pavel A. Akimov ◽  
Taymuraz B. Kaytukov
Keyword(s):  
Structural Analysis ◽  
Three Dimensional ◽  
Grid Method ◽  
Discrete Analogue ◽  
Algebraic Equations ◽  
Initial State ◽  
Haar Basis ◽  
Linear Algebraic Equations ◽  
Gauss Method ◽  
Original Grid

he distinctive paper is devoted to so-called multigrid (particularly two-grid) method of structural analysis based on discrete Haar basis (one-dimensional, two-dimensional and three-dimensional problems are under consideration). Approximations of the mesh functions in discrete Haar bases of zero and first levels are described (the mesh function is represented as the sum in which one term is its approximation of the first level, and the second term is so-called complement (up to the initial state) on the grid of the first level). Special projectors are constructed for the spaces of vector functions of the original grid to the space of their approximation on the first-level grid and its complement (the refinement component) to the initial state. Basic scheme of the two-grid method is presented. This method allows solution of boundary problems of structural mechanics with the use of matrix operators of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation is a system of linear algebraic equations which is constructed with the use of finite element method or finite difference method. Block Gauss method can be used for direct solution.

On weak non-equivalence of wavelet–like systems in L1

2008 ◽  
Vol 144 (2) ◽  
pp. 499-510 ◽  
Author(s):  
SMBAT GOGYAN ◽  
P. WOJTASZCZYK
Keyword(s):  
Type System ◽  
Haar Wavelet ◽  
Wavelet Basis ◽  
Haar Basis

AbstractWe show that in $L_1(\R)$ the Haar wavelet basis is not equivalent to any permutation with any signs of the Strω wavelet basis. We also construct a Haar-type system in L1[0,1] which is not equivalent to any subsequence with signs of the classical Haar basis.

RESOLUTION OF AN INVERSE PROBLEM BY HAAR BASIS AND LEGENDRE WAVELET METHODS

2013 ◽  
Vol 11 (05) ◽  
pp. 1350034 ◽  
Author(s):  
REZA POURGHOLI ◽  
AMIN ESFAHANI ◽  
SAEDEH FOADIAN ◽  
SONA PAREHKAR
Keyword(s):  
Inverse Problem ◽  
Noisy Data ◽  
The Body ◽  
Tikhonov Regularization Method ◽  
Haar Basis ◽  
Cpu Time ◽  
Exponential Rate Of Convergence ◽  
Ill Posed ◽  
Wavelet Methods ◽  
Dual Core

In this paper, two numerical methods are presented to solve an ill-posed inverse problem for Fisher's equation using noisy data. These two methods are the Haar basis and the Legendre wavelet methods combined with the Tikhonov regularization method. A sensor located at a point inside the body is used and u(x, t) at a point x = a, 0 < a < 1 is measured and these methods are applied to the inverse problem. We also show that an exponential rate of convergence of these methods. In fact, this work considers a comparative study between the Haar basis and the Legendre wavelet methods to solve some ill-posed inverse problems. Results show that an excellent estimation of the unknown function of the inverse problem which have been obtained within a couple of minutes CPU time at Pentium(R) Dual-Core CPU 2.20 GHz.

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