Approximation Properties of the Vector Weak Rescaled Pure Greedy Algorithm

We first study the error performances of the Vector Weak Rescaled Pure Greedy Algorithm for simultaneous approximation with respect to a dictionary D in a Hilbert space. We show that the convergence rate of the Vector Weak Rescaled Pure Greedy Algorithm on A1(D) and the closure of the convex hull of...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Mathematics (Basel) Ročník 11; číslo 9; s. 2020
Hlavní autori: Xu, Xu, Guo, Jinyu, Ye, Peixin, Zhang, Wenhui
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 24.04.2023
Predmet:
Algorithms
Analysis
Approximation
Banach spaces
Chebyshev approximation
Computational geometry
Convergence
Convexity
Dictionaries
Efficiency
Error analysis
Food science
greedy algorithm
Greedy algorithms
Hilbert space
Hilbert spaces
Machine learning
Mathematical analysis
modulus of smoothness
Signal processing
uniformly smooth Banach spaces
vector approximation
ISSN:2227-7390, 2227-7390
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:We first study the error performances of the Vector Weak Rescaled Pure Greedy Algorithm for simultaneous approximation with respect to a dictionary D in a Hilbert space. We show that the convergence rate of the Vector Weak Rescaled Pure Greedy Algorithm on A1(D) and the closure of the convex hull of the dictionary D is optimal. The Vector Weak Rescaled Pure Greedy Algorithm has some advantages. It has a weaker convergence condition and a better convergence rate than the Vector Weak Pure Greedy Algorithm and is simpler than the Vector Weak Orthogonal Greedy Algorithm. Then, we design a Vector Weak Rescaled Pure Greedy Algorithm in a uniformly smooth Banach space setting. We obtain the convergence properties and error bound of the Vector Weak Rescaled Pure Greedy Algorithm in this case. The results show that the convergence rate of the VWRPGA on A1(D) is sharp. Similarly, the Vector Weak Rescaled Pure Greedy Algorithm is simpler than the Vector Weak Chebyshev Greedy Algorithm and the Vector Weak Relaxed Greedy Algorithm.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math11092020