On the Approximate Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces
We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak...
Ausführliche Beschreibung
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| Autor*in: |
Dereventsov, A.V. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016transfer abstract |
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| Schlagwörter: |
Approximate Weak Chebyshev Greedy Algorithm |
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| Umfang: |
17 |
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| Übergeordnetes Werk: |
Enthalten in: In silico drug repurposing in COVID-19: A network-based analysis - Sibilio, Pasquale ELSEVIER, 2021, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:436 ; year:2016 ; number:1 ; day:1 ; month:04 ; pages:288-304 ; extent:17 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.jmaa.2015.12.006 |
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| 520 | |a We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. | ||
| 520 | |a We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. | ||
| 650 | 7 | |a Approximate Weak Chebyshev Greedy Algorithm |2 Elsevier | |
| 650 | 7 | |a Greedy algorithm |2 Elsevier | |
| 650 | 7 | |a Weak Chebyshev Greedy Algorithm |2 Elsevier | |
| 650 | 7 | |a Banach space |2 Elsevier | |
| 650 | 7 | |a Nonlinear approximation |2 Elsevier | |
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10.1016/j.jmaa.2015.12.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001927.pica (DE-627)ELV019867654 (ELSEVIER)S0022-247X(15)01112-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Dereventsov, A.V. verfasserin aut On the Approximate Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces 2016transfer abstract 17 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. Approximate Weak Chebyshev Greedy Algorithm Elsevier Greedy algorithm Elsevier Weak Chebyshev Greedy Algorithm Elsevier Banach space Elsevier Nonlinear approximation Elsevier Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:436 year:2016 number:1 day:1 month:04 pages:288-304 extent:17 https://doi.org/10.1016/j.jmaa.2015.12.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 436 2016 1 1 0401 288-304 17 |
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10.1016/j.jmaa.2015.12.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001927.pica (DE-627)ELV019867654 (ELSEVIER)S0022-247X(15)01112-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Dereventsov, A.V. verfasserin aut On the Approximate Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces 2016transfer abstract 17 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. Approximate Weak Chebyshev Greedy Algorithm Elsevier Greedy algorithm Elsevier Weak Chebyshev Greedy Algorithm Elsevier Banach space Elsevier Nonlinear approximation Elsevier Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:436 year:2016 number:1 day:1 month:04 pages:288-304 extent:17 https://doi.org/10.1016/j.jmaa.2015.12.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 436 2016 1 1 0401 288-304 17 |
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10.1016/j.jmaa.2015.12.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001927.pica (DE-627)ELV019867654 (ELSEVIER)S0022-247X(15)01112-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Dereventsov, A.V. verfasserin aut On the Approximate Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces 2016transfer abstract 17 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. Approximate Weak Chebyshev Greedy Algorithm Elsevier Greedy algorithm Elsevier Weak Chebyshev Greedy Algorithm Elsevier Banach space Elsevier Nonlinear approximation Elsevier Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:436 year:2016 number:1 day:1 month:04 pages:288-304 extent:17 https://doi.org/10.1016/j.jmaa.2015.12.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 436 2016 1 1 0401 288-304 17 |
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10.1016/j.jmaa.2015.12.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001927.pica (DE-627)ELV019867654 (ELSEVIER)S0022-247X(15)01112-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Dereventsov, A.V. verfasserin aut On the Approximate Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces 2016transfer abstract 17 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. Approximate Weak Chebyshev Greedy Algorithm Elsevier Greedy algorithm Elsevier Weak Chebyshev Greedy Algorithm Elsevier Banach space Elsevier Nonlinear approximation Elsevier Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:436 year:2016 number:1 day:1 month:04 pages:288-304 extent:17 https://doi.org/10.1016/j.jmaa.2015.12.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 436 2016 1 1 0401 288-304 17 |
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10.1016/j.jmaa.2015.12.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001927.pica (DE-627)ELV019867654 (ELSEVIER)S0022-247X(15)01112-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Dereventsov, A.V. verfasserin aut On the Approximate Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces 2016transfer abstract 17 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. Approximate Weak Chebyshev Greedy Algorithm Elsevier Greedy algorithm Elsevier Weak Chebyshev Greedy Algorithm Elsevier Banach space Elsevier Nonlinear approximation Elsevier Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:436 year:2016 number:1 day:1 month:04 pages:288-304 extent:17 https://doi.org/10.1016/j.jmaa.2015.12.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 436 2016 1 1 0401 288-304 17 |
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The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. 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On the Approximate Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces |
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We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. |
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We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. |
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We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in , is defined for any Banach space X and a dictionary D , and provides nonlinear n-term approximation with respect to D . In this paper we study the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) – a modification of the WCGA that was studied in . In the AWCGA we are allowed to calculate n-term approximation with a perturbation in computing the norming functional and a relative error in calculating the approximant. Such permission is natural for the numerical applications and simplifies realization of the algorithm. We obtain conditions that are necessary and sufficient for the convergence of the AWCGA for any element of X. In particular, we show that if perturbations and errors are from ℓ 1 space then the conditions for the convergence of the AWCGA are the same as for the WCGA. For specifically chosen perturbations and errors we estimate the rate of convergence for any element f from the closure of the convex hull of D and demonstrate that in special cases the AWCGA performs as well as the WCGA. |
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