Geodesic
On $n$-Term Approximation with Positive Coefficients
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 373-382

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In this paper, we consider algorithms for constructing $n$-terms approximations with nonnegative coefficients. The convergence theorem is proved for a “positive” analog of the Pure Greedy Algorithm. We establish a condition on the sequence of weakness coefficients which is sufficient for the convergence of the Positive Weak Greedy Algorithm. This condition is also necessary for the class of monotone sequences.
Mots-clés : polynomial approximation
Keywords: greedy algorithm, approximation theory, positive dictionary, redundant system. 
@article{MZM_2007_82_3_a4,
     author = {E. D. Livshits},
     title = {On $n${-Term} {Approximation} with {Positive} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {373--382},
     publisher = {mathdoc},
     volume = {82},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a4/}
}
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E. D. Livshits. On $n$-Term Approximation with Positive Coefficients. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 373-382. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a4/