caa a22 4500 467939381 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10444-004-7613-4 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7613-4 Simultaneous approximation by greedy algorithms [Elektronische Daten] [D. Leviatan, V. Temlyakov] We study nonlinear m-term approximation with regard to a redundant dictionary $\mathcal {D}$ in a Hilbert space H. It is known that the Pure Greedy Algorithm (or, more generally, the Weak Greedy Algorithm) provides for each f∈H and any dictionary $\mathcal {D}$ an expansion into a series $$f=\sum_{j=1}^{\infty}c_{j}(f)\varphi_{j}(f),\quad\varphi_{j}(f)\in \mathcal {D},\ j=1,2,\ldots,$$ with the Parseval property: ‖f‖2=∑j|cj(f)|2. Following the paper of A. Lutoborski and the second author we study analogs of the above expansions for a given finite number of functions f1,. . .,fN with a requirement that the dictionary elements φj of these expansions are the same for all fi, i=1,. . .,N. We study convergence and rate of convergence of such expansions which we call simultaneous expansions. Springer, 2006 greedy algorithms nationallicence convergence nationallicence simultaneous approximation nationallicence Leviatan D. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel aut Temlyakov V. Department of Mathematics, University of South Carolina, SC 29208, Columbia, USA aut Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 73-90 1019-7168 25:1-3<73 2006 25 10444 https://doi.org/10.1007/s10444-004-7613-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7613-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Leviatan D. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel aut NATIONALLICENCE 700 1- Temlyakov V. Department of Mathematics, University of South Carolina, SC 29208, Columbia, USA aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 73-90 1019-7168 25:1-3<73 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer