On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis
We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for L 1 [0,1] d ( d ≥1). We prove convergence and uniform boundedness of the weak greedy approximants for all f ∈ L 1 [0,1] d .
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| Vydáno v: | Constructive approximation Ročník 39; číslo 2; s. 343 - 366 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Boston
Springer US
01.04.2014
|
| Témata: | |
| ISSN: | 0176-4276, 1432-0940 |
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| Abstract | We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for
L
1
[0,1]
d
(
d
≥1). We prove convergence and uniform boundedness of the weak greedy approximants for all
f
∈
L
1
[0,1]
d
. |
|---|---|
| AbstractList | We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for
L
1
[0,1]
d
(
d
≥1). We prove convergence and uniform boundedness of the weak greedy approximants for all
f
∈
L
1
[0,1]
d
. |
| Author | Gogyan, S. Kutzarova, Denka Dilworth, S. J. |
| Author_xml | – sequence: 1 givenname: S. J. surname: Dilworth fullname: Dilworth, S. J. email: dilworth@math.sc.edu organization: Department of Mathematics, University of South Carolina – sequence: 2 givenname: S. surname: Gogyan fullname: Gogyan, S. organization: Institute of Mathematics, Armenian Academy of Sciences – sequence: 3 givenname: Denka surname: Kutzarova fullname: Kutzarova, Denka organization: Institute of Mathematics, Bulgarian Academy of Sciences, Department of Mathematics, University of Illinois at Urbana-Champaign |
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| Cites_doi | 10.1017/CBO9780511762291 10.1006/jath.2000.3512 10.1023/A:1018900431309 10.1016/j.jfa.2012.09.011 10.1006/jath.2001.3641 10.1016/j.jat.2008.08.017 10.1007/s003659900090 |
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| Issue | 2 |
| Keywords | Greedy algorithms Multivariate Haar system Multivariate Haar wavelet 42A10 Branch-greedy 41A65 46B20 Thresholding greedy algorithm Weak thresholding Nonlinear approximation |
| Language | English |
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| References | Gogyan (CR4) 2009; 161 Dilworth, Kutzarova, Wojtaszczyk (CR3) 2002; 114 Wojtaszczyk (CR11) 2000; 107 Konyagin, Temlyakov (CR5) 1999; 5 Temlyakov (CR9) 2007 Dilworth, Kutzarova, Schlumprecht, Wojtaszczyk (CR2) 2012; 263 Temlyakov (CR10) 2011 Konyagin, Temlyakov (CR6) 2002; 28 Bénéteau, van Fleet (CR1) 2011; 58 Temlyakov (CR7) 1998; 14 Temlyakov (CR8) 1998; 8 C. Bénéteau (9212_CR1) 2011; 58 P. Wojtaszczyk (9212_CR11) 2000; 107 S.V. Konyagin (9212_CR5) 1999; 5 V.N. Temlyakov (9212_CR10) 2011 V.N. Temlyakov (9212_CR8) 1998; 8 V.N. Temlyakov (9212_CR9) 2007 S.J. Dilworth (9212_CR2) 2012; 263 V.N. Temlyakov (9212_CR7) 1998; 14 S.V. Konyagin (9212_CR6) 2002; 28 S.J. Dilworth (9212_CR3) 2002; 114 S. Gogyan (9212_CR4) 2009; 161 |
| References_xml | – year: 2011 ident: CR10 publication-title: Greedy Approximation doi: 10.1017/CBO9780511762291 – volume: 107 start-page: 293 year: 2000 end-page: 314 ident: CR11 article-title: Greedy algorithm for general biorthogonal systems publication-title: J. Approx. Theory doi: 10.1006/jath.2000.3512 – volume: 58 start-page: 655 issue: 5 year: 2011 end-page: 666 ident: CR1 article-title: Discrete wavelet transformations and undergraduate education publication-title: Not. Am. Math. Soc. – volume: 8 start-page: 249 year: 1998 end-page: 265 ident: CR8 article-title: The best -term approximation and greedy algorithms publication-title: Adv. Comput. Math. doi: 10.1023/A:1018900431309 – volume: 28 start-page: 305 year: 2002 end-page: 328 ident: CR6 article-title: Greedy approximation with regard to bases and general minimal systems publication-title: Serdica Math. J. – volume: 263 start-page: 3900 year: 2012 end-page: 3921 ident: CR2 article-title: Weak thresholding greedy algorithms in Banach spaces publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2012.09.011 – volume: 114 start-page: 214 year: 2002 end-page: 241 ident: CR3 article-title: On approximate systems in Banach spaces publication-title: J. Approx. Theory doi: 10.1006/jath.2001.3641 – volume: 161 start-page: 49 year: 2009 end-page: 64 ident: CR4 article-title: On convergence of weak thresholding greedy algorithm in (0,1) publication-title: J. Approx. Theory doi: 10.1016/j.jat.2008.08.017 – volume: 5 start-page: 1 year: 1999 end-page: 15 ident: CR5 article-title: A remark on greedy approximation in Banach spaces publication-title: East J. Approx. – volume: 14 start-page: 569 year: 1998 end-page: 587 ident: CR7 article-title: Greedy approximation and -term trigonometric approximation publication-title: Constr. Approx. doi: 10.1007/s003659900090 – start-page: 1479 year: 2007 end-page: 1504 ident: CR9 article-title: Greedy approximations with regard to bases publication-title: Proc. Int. Cong. of Mathem – volume: 161 start-page: 49 year: 2009 ident: 9212_CR4 publication-title: J. Approx. Theory doi: 10.1016/j.jat.2008.08.017 – volume: 28 start-page: 305 year: 2002 ident: 9212_CR6 publication-title: Serdica Math. J. – volume: 5 start-page: 1 year: 1999 ident: 9212_CR5 publication-title: East J. Approx. – volume: 114 start-page: 214 year: 2002 ident: 9212_CR3 publication-title: J. Approx. Theory doi: 10.1006/jath.2001.3641 – volume-title: Greedy Approximation year: 2011 ident: 9212_CR10 doi: 10.1017/CBO9780511762291 – volume: 107 start-page: 293 year: 2000 ident: 9212_CR11 publication-title: J. Approx. Theory doi: 10.1006/jath.2000.3512 – volume: 263 start-page: 3900 year: 2012 ident: 9212_CR2 publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2012.09.011 – volume: 14 start-page: 569 year: 1998 ident: 9212_CR7 publication-title: Constr. Approx. doi: 10.1007/s003659900090 – volume: 8 start-page: 249 year: 1998 ident: 9212_CR8 publication-title: Adv. Comput. Math. doi: 10.1023/A:1018900431309 – start-page: 1479 volume-title: Proc. Int. Cong. of Mathem year: 2007 ident: 9212_CR9 – volume: 58 start-page: 655 issue: 5 year: 2011 ident: 9212_CR1 publication-title: Not. Am. Math. Soc. |
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L
1
[0,1]
d
(
d
≥1). We prove convergence and uniform boundedness... |
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| Title | On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis |
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