Simultaneous approximation by greedy algorithms
نویسندگان
چکیده
منابع مشابه
Simultaneous approximation by greedy algorithms
We study nonlinear m-term approximation with regard to a redundant dictionary 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 D an expansion into a series f = ∞ X j=1 cj(f)φj(f), φj(f) ∈ D, j = 1, 2, . . . with the Parseval property: ‖f‖2 = j |cj(f)|. Following the paper of A. Lutoborsk...
متن کاملAlgorithms for simultaneous sparse approximation. Part I: Greedy pursuit
A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals that participate. These elementary signals typically model coherent structures in the input signals, and they...
متن کاملGreedy in Approximation Algorithms
The objective of this paper is to characterize classes of problems for which a greedy algorithm finds solutions provably close to optimum. To that end, we introduce the notion of k-extendible systems, a natural generalization of matroids, and show that a greedy algorithm is a 1 k -factor approximation for these systems. Many seemly unrelated problems fit in our framework, e.g.: b-matching, maxi...
متن کاملApproximation and learning by greedy algorithms
We consider the problem of approximating a given element f from a Hilbert space H by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the existing theory of convergence rates for both the orthogonal greedy algorithm and the relaxed greedy algorithm, as well as for the forward stepwise projection algorithm. ...
متن کاملSimultaneous greedy approximation in Banach spaces
We study nonlinear m-term approximation with regard to a redundant dictionary D in a Banach space. It is known that in the case of Hilbert space H the pure greedy algorithm (or, more generally, the weak greedy algorithm) provides for each f ∈ H and any dictionaryD an expansion into a series f = ∞ ∑ j=1 cj (f ) j (f ), j (f ) ∈ D, j = 1, 2, . . . with the Parseval property: ‖f ‖2 = ∑j |cj (f )|2...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2006
ISSN: 1019-7168,1572-9044
DOI: 10.1007/s10444-004-7613-4