The WCGA in Lp(logL)α Spaces

We present some new results concerning Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces X . First, we generalize Temlyakov’s theorem (Temlyakov in Forum Math Sigma 2(12):26, 2014) to cover situations in which the modulus of smoothness and th...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Constructive approximation Ročník 61; číslo 1; s. 115 - 147
Hlavný autor: Garrigós, Gustavo
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.02.2025
Springer Nature B.V
Predmet:
Algorithms
Analysis
Approximation
Banach spaces
Chebyshev approximation
Dictionaries
Greedy algorithms
Mathematics
Mathematics and Statistics
Numerical Analysis
Smoothness
Theorems
41A46
46B15
Trigonometric system
41A25
Non-linear approximation
46E30
Uniformly smooth Banach space
41A65
Greedy algorithm
46B20
Orlicz space
Haar system
ISSN:0176-4276, 1432-0940
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:We present some new results concerning Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces X . First, we generalize Temlyakov’s theorem (Temlyakov in Forum Math Sigma 2(12):26, 2014) to cover situations in which the modulus of smoothness and the A 3 parameter are not necessarily power functions. Secondly, we apply this new theorem to the Zygmund spaces X = L p ( log L ) α , with 1 < p < ∞ and α ∈ R , and show that, when the Haar system is used, then exact recovery of N -sparse signals occurs when the number of iterations is ϕ ( N ) = O ( N max { 1 , 2 / p ′ } ( log N ) | α | p ′ ) . Moreover, this quantity is sharp when p ≤ 2 . Finally, an expression for ϕ ( N ) in the case of the trigonometric system is also given.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-023-09664-y