Greedy approximation
In this survey we discuss properties of specific methods of approximation that belong to a family of greedy approximation methods (greedy algorithms). It is now well understood that we need to study nonlinear sparse representations in order to significantly increase our ability to process (compress,...
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| Published in | Acta numerica Vol. 17; pp. 235 - 409 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.05.2008
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0962-4929 1474-0508 |
| DOI | 10.1017/S0962492906380014 |
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| Abstract | In this survey we discuss properties of specific methods of approximation that belong to a family of greedy approximation methods (greedy algorithms). It is now well understood that we need to study nonlinear sparse representations in order to significantly increase our ability to process (compress, denoise, etc.) large data sets. Sparse representations of a function are not only a powerful analytic tool but they are utilized in many application areas such as image/signal processing and numerical computation. The key to finding sparse representations is the concept of m-term approximation of the target function by the elements of a given system of functions (dictionary). The fundamental question is how to construct good methods (algorithms) of approximation. Recent results have established that greedy-type algorithms are suitable methods of nonlinear approximation in both m-term approximation with regard to bases, and m-term approximation with regard to redundant systems. It turns out that there is one fundamental principle that allows us to build good algorithms, both for arbitrary redundant systems and for very simple well-structured bases, such as the Haar basis. This principle is the use of a greedy step in searching for a new element to be added to a given m-term approximant. |
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| AbstractList | In this survey we discuss properties of specific methods of approximation that belong to a family of greedy approximation methods (greedy algorithms). It is now well understood that we need to study nonlinear sparse representations in order to significantly increase our ability to process (compress, denoise, etc.) large data sets. Sparse representations of a function are not only a powerful analytic tool but they are utilized in many application areas such as image/signal processing and numerical computation. The key to finding sparse representations is the concept of m-term approximation of the target function by the elements of a given system of functions (dictionary). The fundamental question is how to construct good methods (algorithms) of approximation. Recent results have established that greedy-type algorithms are suitable methods of nonlinear approximation in both m-term approximation with regard to bases, and m-term approximation with regard to redundant systems. It turns out that there is one fundamental principle that allows us to build good algorithms, both for arbitrary redundant systems and for very simple well-structured bases, such as the Haar basis. This principle is the use of a greedy step in searching for a new element to be added to a given m-term approximant. [PUBLICATION ABSTRACT] In this survey we discuss properties of specific methods of approximation that belong to a family of greedy approximation methods (greedy algorithms). It is now well understood that we need to study nonlinear sparse representations in order to significantly increase our ability to process (compress, denoise, etc. ) large data sets. Sparse representations of a function are not only a powerful analytic tool but they are utilized in many application areas such as image/signal processing and numerical computation. The key to finding sparse representations is the concept of m -term approximation of the target function by the elements of a given system of functions (dictionary). The fundamental question is how to construct good methods (algorithms) of approximation. Recent results have established that greedy-type algorithms are suitable methods of nonlinear approximation in both m -term approximation with regard to bases, and m -term approximation with regard to redundant systems. It turns out that there is one fundamental principle that allows us to build good algorithms, both for arbitrary redundant systems and for very simple well-structured bases, such as the Haar basis. This principle is the use of a greedy step in searching for a new element to be added to a given m -term approximant. In this survey we discuss properties of specific methods of approximation that belong to a family of greedy approximation methods (greedy algorithms). It is now well understood that we need to study nonlinear sparse representations in order to significantly increase our ability to process (compress, denoise, etc.) large data sets. Sparse representations of a function are not only a powerful analytic tool but they are utilized in many application areas such as image/signal processing and numerical computation. The key to finding sparse representations is the concept of m-term approximation of the target function by the elements of a given system of functions (dictionary). The fundamental question is how to construct good methods (algorithms) of approximation. Recent results have established that greedy-type algorithms are suitable methods of nonlinear approximation in both m-term approximation with regard to bases, and m-term approximation with regard to redundant systems. It turns out that there is one fundamental principle that allows us to build good algorithms, both for arbitrary redundant systems and for very simple well-structured bases, such as the Haar basis. This principle is the use of a greedy step in searching for a new element to be added to a given m-term approximant. |
| Author | Temlyakov, V. N. |
| Author_xml | – sequence: 1 givenname: V. N. surname: Temlyakov fullname: Temlyakov, V. N. email: temlyak@math.sc.edu organization: University of South Carolina, Columbia, 29208, USA E-mail: temlyak@math.sc.edu |
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| Cites_doi | 10.1007/s003659910004 10.1007/s102080010029 10.1007/BFb0078887 10.1007/978-3-642-66557-8 10.1137/S003614450037906X 10.1016/S1063-5203(03)00023-X 10.1007/BF02421317 10.7169/facm/1538186665 10.1007/s10208-008-9031-3 10.1007/s003659900060 10.1023/A:1023261910883 10.1007/978-3-662-02888-9 10.1007/BF01456804 10.1007/BF02514500 10.1016/S0021-9045(03)00133-3 10.1109/18.256500 10.1007/BF01198113 10.1007/BF01208903 10.1109/TIT.2005.858979 10.1109/TIT.2006.871582 10.1007/978-3-642-65711-5 10.1016/j.jco.2004.09.004 10.1016/S0885-064X(02)00025-0 10.1007/s10476-005-0007-0 10.1017/CBO9780511721571.012 10.1093/biomet/81.3.425 10.1016/0022-1236(90)90137-A 10.1134/S0001434607110193 10.1016/j.jat.2007.01.004 10.1214/aos/1176350382 10.1007/s003659910017 10.4064/sm159-2-1 10.1109/TIT.2004.834793 10.1007/s10444-004-7613-4 10.1007/s00365-003-0533-6 10.1023/A:1016657209416 10.1006/jcom.1997.0458 10.1007/s00041-002-0023-4 10.1017/CBO9780511565984 10.1006/jath.2000.3512 10.1006/jath.1998.3265 10.1007/s10444-005-7452-y 10.1137/S0036141097320705 10.1023/A:1016061804993 10.1215/ijm/1256046370 10.1007/s00365-002-0525-y 10.1023/A:1012255021470 10.1109/78.258082 10.1007/BF01449770 10.1023/A:1018900431309 10.1214/aos/1176349519 10.4064/sm159-1-7 10.1007/s003650010032 10.1007/BF02678430 10.1007/BF02124742 10.1002/cpa.20124 10.4064/sm159-1-4 10.1007/BFb0078875 10.4064/bc72-0-25 10.1007/s10208-002-0056-8 10.2307/2374796 10.5802/afst.257 10.1007/BF01274186 10.4064/aa96-3-7 10.1007/s00041-001-4021-8 10.4064/bc72-0-23 10.1007/s003659900090 10.1007/BF02403043 10.1007/s00041-006-6033-x 10.4064/sm161-3-1 10.1109/18.556601 10.1070/SM1989v062n01ABEH003228 10.4064/sm-89-1-79-103 10.1214/aos/1176348546 10.1006/jath.2001.3641 10.1007/BF02678464 10.1090/S0273-0979-01-00923-5 10.1007/s00365-004-0565-6 10.1007/s10208-004-0158-6 10.2307/2118587 10.1007/BF02392215 10.1007/BF02386041 10.1016/0022-1236(81)90076-8 10.1007/s00365-002-0514-1 10.1214/aos/1069362377 10.1007/BF01262187 10.1109/18.119732 10.1007/s00365-003-0556-z 10.1007/s11006-005-0113-0 10.1080/01621459.1981.10477729 10.1023/A:1018917218956 10.1006/acha.1993.1008 10.1109/TIT.2005.860430 10.1017/CBO9780511662447 10.1016/S0885-064X(03)00026-8 10.1007/BF02808215 10.1007/s00365-006-0633-8 |
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| References | S0962492906380014_ref132 S0962492906380014_ref099 S0962492906380014_ref011 S0962492906380014_ref133 S0962492906380014_ref012 S0962492906380014_ref130 S0962492906380014_ref097 S0962492906380014_ref098 Konyagin (S0962492906380014_ref076) 2002; 28 S0962492906380014_ref010 S0962492906380014_ref015 S0962492906380014_ref137 S0962492906380014_ref016 Wojtaszczyk (S0962492906380014_ref146) 2002; XXX S0962492906380014_ref134 S0962492906380014_ref013 Maiorov (S0962492906380014_ref096) 2002 S0962492906380014_ref014 S0962492906380014_ref092 Lee (S0962492906380014_ref085) 1996; 42 S0962492906380014_ref095 Temlyakov (S0962492906380014_ref112) 1990; 3 Tropp (S0962492906380014_ref142) 2005 S0962492906380014_ref094 Gribonval (S0962492906380014_ref059) 2001; 7 S0962492906380014_ref019 S0962492906380014_ref138 S0962492906380014_ref017 S0962492906380014_ref139 S0962492906380014_ref018 DeVore (S0962492906380014_ref028) 2003; 3 Livshitz (S0962492906380014_ref091) 2007; 198 Konyagin (S0962492906380014_ref074) 1999; 5 S0962492906380014_ref023 S0962492906380014_ref144 S0962492906380014_ref020 S0962492906380014_ref141 S0962492906380014_ref147 S0962492906380014_ref026 S0962492906380014_ref027 S0962492906380014_ref148 S0962492906380014_ref025 Baishanski (S0962492906380014_ref003) 1983; 27 Candèes (S0962492906380014_ref009) 2006; 3 DeVore (S0962492906380014_ref021) 1998; 7 S0962492906380014_ref029 Stromberg (S0962492906380014_ref108) 2003; 14 S0962492906380014_ref077 S0962492906380014_ref111 S0962492906380014_ref078 Poggio (S0962492906380014_ref104) 2003; 50 Traub (S0962492906380014_ref140) 1988 Kashin (S0962492906380014_ref069) 1985; 172 S0962492906380014_ref114 Livshitz (S0962492906380014_ref093) 2001; 232 S0962492906380014_ref113 S0962492906380014_ref070 S0962492906380014_ref071 S0962492906380014_ref118 S0962492906380014_ref119 S0962492906380014_ref116 Temlyakov (S0962492906380014_ref129) 2004; 10 S0962492906380014_ref121 Temlyakov (S0962492906380014_ref115) 1993; 4 S0962492906380014_ref088 Konyagin (S0962492906380014_ref079) 2004 S0962492906380014_ref122 S0962492906380014_ref001 S0962492906380014_ref089 S0962492906380014_ref086 S0962492906380014_ref120 S0962492906380014_ref087 S0962492906380014_ref125 S0962492906380014_ref005 S0962492906380014_ref123 S0962492906380014_ref002 S0962492906380014_ref124 S0962492906380014_ref080 S0962492906380014_ref081 S0962492906380014_ref084 S0962492906380014_ref082 Temlyakov (S0962492906380014_ref131) 2005; 248 S0962492906380014_ref083 Sil'nichenko (S0962492906380014_ref106) 2004; 76 Bary (S0962492906380014_ref004) 1961 Wojtaszczyk (S0962492906380014_ref145) 2002 S0962492906380014_ref008 S0962492906380014_ref127 S0962492906380014_ref006 S0962492906380014_ref128 Livshitz (S0962492906380014_ref090) 2006; 70 S0962492906380014_ref055 S0962492906380014_ref053 DeVore (S0962492906380014_ref024) 2004 S0962492906380014_ref057 S0962492906380014_ref058 Temlyakov (S0962492906380014_ref126) 2002 S0962492906380014_ref052 Gogyan (S0962492906380014_ref056) 2005; 11 Temlyakov (S0962492906380014_ref136) 2006 S0962492906380014_ref050 Konyagin (S0962492906380014_ref073) 2001; 69 S0962492906380014_ref066 S0962492906380014_ref067 S0962492906380014_ref100 Habala (S0962492906380014_ref060) 1996; I S0962492906380014_ref064 S0962492906380014_ref065 S0962492906380014_ref103 S0962492906380014_ref101 Kerkyacharian (S0962492906380014_ref072) 2006; 12 S0962492906380014_ref102 S0962492906380014_ref062 S0962492906380014_ref063 S0962492906380014_ref061 Wojtaszczyk (S0962492906380014_ref143) 1997; 13 S0962492906380014_ref105 S0962492906380014_ref033 S0962492906380014_ref034 S0962492906380014_ref031 S0962492906380014_ref032 S0962492906380014_ref037 S0962492906380014_ref038 S0962492906380014_ref035 S0962492906380014_ref036 Temlyakov (S0962492906380014_ref110) 1989; 1 S0962492906380014_ref030 Zygmund (S0962492906380014_ref149) 1959 Konyagin (S0962492906380014_ref075) 1999; 5 Galatenko (S0962492906380014_ref051) 2003; 9 S0962492906380014_ref039 S0962492906380014_ref044 Birman (S0962492906380014_ref007) 1977; 32 S0962492906380014_ref045 S0962492906380014_ref042 S0962492906380014_ref043 Temlyakov (S0962492906380014_ref117) 1998; 4 S0962492906380014_ref048 Temlyakov (S0962492906380014_ref109) 1988; 43 S0962492906380014_ref049 S0962492906380014_ref046 S0962492906380014_ref047 DeVore (S0962492906380014_ref022) 2006; 1 S0962492906380014_ref040 S0962492906380014_ref041 Kashin (S0962492906380014_ref068) 1977; 41 Garnaev (S0962492906380014_ref054) 1984; 277 Smithies (S0962492906380014_ref107) 1937; 43 Temlyakov (S0962492906380014_ref135) 2006; 2 |
| References_xml | – volume: 5 start-page: 1 year: 1999 ident: S0962492906380014_ref074 article-title: A remark on greedy approximation in Banach spaces publication-title: East J. Approx. – volume: 43 start-page: 255 year: 1937 ident: S0962492906380014_ref107 article-title: The eigen-values and singular values of integral equations publication-title: Proc. London Math. Soc. – ident: S0962492906380014_ref015 doi: 10.1007/s003659910004 – ident: S0962492906380014_ref127 doi: 10.1007/s102080010029 – ident: S0962492906380014_ref103 doi: 10.1007/BFb0078887 – ident: S0962492906380014_ref088 doi: 10.1007/978-3-642-66557-8 – ident: S0962492906380014_ref013 doi: 10.1137/S003614450037906X – volume: 14 start-page: 257 year: 2003 ident: S0962492906380014_ref108 article-title: Grassmannian frames with applications to coding and communications publication-title: Appl. Comput. Harm. Anal. doi: 10.1016/S1063-5203(03)00023-X – ident: S0962492906380014_ref049 doi: 10.1007/BF02421317 – volume: 2 start-page: 1479 year: 2006 ident: S0962492906380014_ref135 article-title: Greedy approximations with regard to bases publication-title: Proc. International Congress of Mathematics – volume: XXX start-page: 127 year: 2002 ident: S0962492906380014_ref146 article-title: Existence of best m-term approximation publication-title: Functiones et Approximatio doi: 10.7169/facm/1538186665 – ident: S0962492906380014_ref098 doi: 10.1007/s10208-008-9031-3 – volume: 1 start-page: 1 year: 1989 ident: S0962492906380014_ref110 article-title: Approximation of functions with bounded mixed derivative publication-title: Proc. Steklov Inst. – ident: S0962492906380014_ref026 doi: 10.1007/s003659900060 – volume: 32 start-page: 17 year: 1977 ident: S0962492906380014_ref007 article-title: Estimates of singular numbers of integral operators publication-title: Uspekhi Mat. Nauk – volume-title: Trigonometric Series year: 1961 ident: S0962492906380014_ref004 – ident: S0962492906380014_ref089 doi: 10.1023/A:1023261910883 – ident: S0962492906380014_ref122 – ident: S0962492906380014_ref027 doi: 10.1007/978-3-662-02888-9 – ident: S0962492906380014_ref148 doi: 10.1007/BF01456804 – ident: S0962492906380014_ref102 doi: 10.1007/BF02514500 – ident: S0962492906380014_ref053 doi: 10.1016/S0021-9045(03)00133-3 – volume: 7 start-page: 267 year: 2001 ident: S0962492906380014_ref059 article-title: Some remarks on non-linear approximation with Schauder bases publication-title: East J. Approx. – ident: S0962492906380014_ref001 doi: 10.1109/18.256500 – ident: S0962492906380014_ref099 doi: 10.1007/BF01198113 – ident: S0962492906380014_ref113 doi: 10.1007/BF01208903 – ident: S0962492906380014_ref011 doi: 10.1109/TIT.2005.858979 – ident: S0962492906380014_ref041 doi: 10.1109/TIT.2006.871582 – ident: S0962492906380014_ref101 doi: 10.1007/978-3-642-65711-5 – volume: 43 start-page: 770 year: 1988 ident: S0962492906380014_ref109 article-title: Approximation by elements of a finite dimensional subspace of functions from various Sobolev or Nikol'skii spaces publication-title: Matem. Zametki – ident: S0962492906380014_ref086 doi: 10.1016/j.jco.2004.09.004 – volume: 5 start-page: 493 year: 1999 ident: S0962492906380014_ref075 article-title: Rate of convergence of pure greedy algorithms publication-title: East J. Approx. – ident: S0962492906380014_ref128 doi: 10.1016/S0885-064X(02)00025-0 – volume: 76 start-page: 628 year: 2004 ident: S0962492906380014_ref106 article-title: Rate of convergence of greedy algorithms publication-title: Mat. Zametki – ident: S0962492906380014_ref080 doi: 10.1007/s10476-005-0007-0 – ident: S0962492906380014_ref134 doi: 10.1017/CBO9780511721571.012 – ident: S0962492906380014_ref044 doi: 10.1093/biomet/81.3.425 – ident: S0962492906380014_ref016 – volume: 69 start-page: 699 year: 2001 ident: S0962492906380014_ref073 article-title: Comparison of the L1-norms of total and truncated exponential sums publication-title: Mat. Zametki – volume: 248 start-page: 255 year: 2005 ident: S0962492906380014_ref131 article-title: Greedy algorithms with restricted depth search publication-title: Proc. Steklov Inst. Math. – ident: S0962492906380014_ref048 doi: 10.1016/0022-1236(90)90137-A – ident: S0962492906380014_ref070 doi: 10.1134/S0001434607110193 – volume: 3 start-page: 221 year: 1990 ident: S0962492906380014_ref112 article-title: Bilinear approximation and applications publication-title: Proc. Steklov Inst. Math. – ident: S0962492906380014_ref043 doi: 10.1016/j.jat.2007.01.004 – ident: S0962492906380014_ref064 doi: 10.1214/aos/1176350382 – volume: 12 start-page: 103 year: 2006 ident: S0962492906380014_ref072 article-title: Some inequalities for the tensor product of greedy bases and weight-greedy bases publication-title: East J. Approx. – ident: S0962492906380014_ref120 doi: 10.1007/s003659910017 – start-page: 126 volume-title: Approximation Theory: A Volume Dedicated to Borislav Bojanov year: 2004 ident: S0962492906380014_ref079 – ident: S0962492906380014_ref078 doi: 10.4064/sm159-2-1 – ident: S0962492906380014_ref141 doi: 10.1109/TIT.2004.834793 – ident: S0962492906380014_ref087 doi: 10.1007/s10444-004-7613-4 – ident: S0962492906380014_ref094 doi: 10.1007/s00365-003-0533-6 – ident: S0962492906380014_ref123 doi: 10.1023/A:1016657209416 – ident: S0962492906380014_ref032 doi: 10.1006/jcom.1997.0458 – ident: S0962492906380014_ref035 doi: 10.1007/s00041-002-0023-4 – ident: S0962492906380014_ref005 doi: 10.1017/CBO9780511565984 – ident: S0962492906380014_ref144 doi: 10.1006/jath.2000.3512 – ident: S0962492906380014_ref055 – year: 2006 ident: S0962492906380014_ref136 – ident: S0962492906380014_ref119 doi: 10.1006/jath.1998.3265 – volume: 28 start-page: 305 year: 2002 ident: S0962492906380014_ref076 article-title: Greedy approximation with regard to bases and general minimal systems publication-title: Serdica Math. J. – volume: 9 start-page: 43 year: 2003 ident: S0962492906380014_ref051 article-title: On convergence of approximate weak greedy algorithms publication-title: East J. Approx. – ident: S0962492906380014_ref138 doi: 10.1007/s10444-005-7452-y – ident: S0962492906380014_ref018 doi: 10.1137/S0036141097320705 – volume: 3 start-page: 1433 year: 2006 ident: S0962492906380014_ref009 article-title: Compressive sampling publication-title: In Proc. International Congress of Mathematics – ident: S0962492906380014_ref125 doi: 10.1023/A:1016061804993 – volume: 198 start-page: 95 year: 2007 ident: S0962492906380014_ref091 article-title: Optimality of the greedy algorithm for some function classes publication-title: Mat. Sb. – volume: 27 start-page: 449 year: 1983 ident: S0962492906380014_ref003 article-title: Approximation by polynomials of given length publication-title: Illinois J. Math. doi: 10.1215/ijm/1256046370 – ident: S0962492906380014_ref034 doi: 10.1007/s00365-002-0525-y – ident: S0962492906380014_ref058 doi: 10.1023/A:1012255021470 – ident: S0962492906380014_ref097 doi: 10.1109/78.258082 – ident: S0962492906380014_ref105 doi: 10.1007/BF01449770 – volume: 10 start-page: 17 year: 2004 ident: S0962492906380014_ref129 article-title: A remark on simultaneous greedy approximation publication-title: East J. Approx. – volume: 50 start-page: 537 year: 2003 ident: S0962492906380014_ref104 article-title: The mathematics of learning: Dealing with data publication-title: Notices Amer. Math. Soc. – ident: S0962492906380014_ref116 doi: 10.1023/A:1018900431309 – ident: S0962492906380014_ref063 doi: 10.1214/aos/1176349519 – ident: S0962492906380014_ref077 doi: 10.4064/sm159-1-7 – ident: S0962492906380014_ref040 doi: 10.1007/s003650010032 – ident: S0962492906380014_ref100 – start-page: 1 volume-title: Constructive Function Theory year: 2002 ident: S0962492906380014_ref145 – volume: 7 start-page: 51 volume-title: Acta Numerica year: 1998 ident: S0962492906380014_ref021 – ident: S0962492906380014_ref020 doi: 10.1007/BF02678430 – ident: S0962492906380014_ref031 doi: 10.1007/BF02124742 – ident: S0962492906380014_ref010 doi: 10.1002/cpa.20124 – ident: S0962492906380014_ref033 doi: 10.4064/sm159-1-4 – ident: S0962492906380014_ref029 doi: 10.1007/BFb0078875 – ident: S0962492906380014_ref057 – ident: S0962492906380014_ref147 doi: 10.4064/bc72-0-25 – volume: 3 start-page: 161 year: 2003 ident: S0962492906380014_ref028 article-title: Best basis selection for approximation in Lp publication-title: Found. Comput. Math. doi: 10.1007/s10208-002-0056-8 – ident: S0962492906380014_ref023 doi: 10.2307/2374796 – ident: S0962492906380014_ref084 doi: 10.5802/afst.257 – volume-title: Trigonometric Series year: 1959 ident: S0962492906380014_ref149 – ident: S0962492906380014_ref083 doi: 10.1007/BF01274186 – ident: S0962492906380014_ref061 doi: 10.4064/aa96-3-7 – volume: 13 start-page: 1 year: 1997 ident: S0962492906380014_ref143 article-title: On unconditional polynomial bases in Lp and Bergman spaces publication-title: Constr. Approx. – ident: S0962492906380014_ref030 doi: 10.1007/s00041-001-4021-8 – ident: S0962492906380014_ref137 doi: 10.4064/bc72-0-23 – ident: S0962492906380014_ref118 doi: 10.1007/s003659900090 – ident: S0962492906380014_ref002 – ident: S0962492906380014_ref132 – volume: 4 start-page: 245 year: 1993 ident: S0962492906380014_ref115 article-title: Bilinear approximation and related questions publication-title: Proc. Steklov Inst. Math. – ident: S0962492906380014_ref062 doi: 10.1007/BF02403043 – ident: S0962492906380014_ref139 doi: 10.1007/s00041-006-6033-x – ident: S0962492906380014_ref092 – volume: 41 start-page: 334 year: 1977 ident: S0962492906380014_ref068 article-title: Widths of certain finite-dimensional sets and classes of smooth functions publication-title: Izv. Akad. Nauk SSSR, Ser. Mat. – volume-title: On mathematical methods of learning year: 2004 ident: S0962492906380014_ref024 – start-page: 373 volume-title: Approximation Theory X year: 2002 ident: S0962492906380014_ref126 – ident: S0962492906380014_ref067 doi: 10.4064/sm161-3-1 – volume: 42 start-page: 2118 year: 1996 ident: S0962492906380014_ref085 article-title: Efficient agnostic learning of neural networks with bounded fan-in publication-title: IEEE Trans. Inform. Theory doi: 10.1109/18.556601 – ident: S0962492906380014_ref045 – volume: 172 start-page: 187 year: 1985 ident: S0962492906380014_ref069 article-title: On approximation properties of complete orthonormal systems publication-title: Tr. Mat. Inst. Steklova – ident: S0962492906380014_ref111 doi: 10.1070/SM1989v062n01ABEH003228 – ident: S0962492906380014_ref047 doi: 10.4064/sm-89-1-79-103 – start-page: 284 volume-title: Approximation Theory: A Volume Dedicated to Blagovest Sendov year: 2002 ident: S0962492906380014_ref096 – volume: 1 start-page: 187 year: 2006 ident: S0962492906380014_ref022 article-title: Optimal computation publication-title: Proc. International Congress of Mathematics – ident: S0962492906380014_ref006 – ident: S0962492906380014_ref065 doi: 10.1214/aos/1176348546 – ident: S0962492906380014_ref036 doi: 10.1006/jath.2001.3641 – ident: S0962492906380014_ref037 doi: 10.1007/BF02678464 – ident: S0962492906380014_ref019 doi: 10.1090/S0273-0979-01-00923-5 – volume: 232 start-page: 236 year: 2001 ident: S0962492906380014_ref093 article-title: On the convergence of weak greedy algorithms publication-title: Tr. Mat. Inst. Steklova – ident: S0962492906380014_ref130 doi: 10.1007/s00365-004-0565-6 – volume-title: Information-Based Complexity year: 1988 ident: S0962492906380014_ref140 – ident: S0962492906380014_ref025 doi: 10.1007/s10208-004-0158-6 – ident: S0962492906380014_ref082 doi: 10.2307/2118587 – ident: S0962492906380014_ref046 doi: 10.1007/BF02392215 – ident: S0962492906380014_ref014 doi: 10.1007/BF02386041 – volume: 4 start-page: 87 year: 1998 ident: S0962492906380014_ref117 article-title: Nonlinear m-term approximation with regard to the multivariate Haar system publication-title: East J. Approx. – volume: 70 start-page: 95 year: 2006 ident: S0962492906380014_ref090 article-title: On the recursive greedy algorithm publication-title: Izv. RAN. Ser. Mat. – volume: I volume-title: Introduction to Banach Spaces year: 1996 ident: S0962492906380014_ref060 – ident: S0962492906380014_ref012 doi: 10.1016/0022-1236(81)90076-8 – ident: S0962492906380014_ref124 doi: 10.1007/s00365-002-0514-1 – ident: S0962492906380014_ref039 doi: 10.1214/aos/1069362377 – ident: S0962492906380014_ref133 doi: 10.4064/bc72-0-23 – ident: S0962492906380014_ref114 doi: 10.1007/BF01262187 – ident: S0962492906380014_ref017 doi: 10.1109/18.119732 – ident: S0962492906380014_ref071 doi: 10.1007/s00365-003-0556-z – volume: 11 start-page: 221 year: 2005 ident: S0962492906380014_ref056 article-title: Greedy algorithm with regard to Haar subsystems publication-title: East J. Approx. – ident: S0962492906380014_ref052 doi: 10.1007/s11006-005-0113-0 – year: 2005 ident: S0962492906380014_ref142 – ident: S0962492906380014_ref050 doi: 10.1080/01621459.1981.10477729 – ident: S0962492906380014_ref121 doi: 10.1023/A:1018917218956 – ident: S0962492906380014_ref038 doi: 10.1006/acha.1993.1008 – ident: S0962492906380014_ref042 doi: 10.1109/TIT.2005.860430 – ident: S0962492906380014_ref066 doi: 10.1017/CBO9780511662447 – ident: S0962492906380014_ref095 doi: 10.1016/S0885-064X(03)00026-8 – ident: S0962492906380014_ref008 doi: 10.1007/BF02808215 – ident: S0962492906380014_ref081 doi: 10.1007/s00365-006-0633-8 – volume: 277 start-page: 1048 year: 1984 ident: S0962492906380014_ref054 article-title: The widths of a Euclidean ball publication-title: Dokl. Akad. Nauk USSR |
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