Long Jingfan, Ye Peixin, "Weak Greedy Algorithms for Nonlinear Approximation with Quasi-Greedy Bases," WSEAS Transactions on Mathematics, vol. 13, pp. 525-534, 2014, DOI:
Long Jingfan, Ye Peixin. Weak Greedy Algorithms for Nonlinear Approximation with Quasi-Greedy Bases.
WSEAS Transactions on Mathematics. 2014;13:525-534.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
Weak Greedy Algorithms for Nonlinear Approximation with Quasi-Greedy Bases
Authors: ,
Abstract: We study weak greedy approximation with respect to quasi-greedy bases. For a Hilbert space, we prove that the error of the m-th weak greedy approximation is bounded by the error of best m-term approximation mul- tiplied by an extra factor of order lnm. However we show weak greedy algorithm realizes the best expansional m-term approximation for individual element and best m-term approximation for some sparse classes. Further- more we establish sharp Lebesgue-type inequality for expansional m-term approximation with quasi-greedy bases in Banach spaces.
Keywords:
Quasi-greedy basis, Weak greedy algorithm, m-term approximation, Sparse classes, Optimality, Hilbert spaces
Pages: 525-534 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #51 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
×
Citation Tools