On weak greedy algorithms
Theoretical contribution for researchers studying greedy algorithms in approximation theory.
The paper extends results on weak greedy algorithms from scalar parameter to weakness sequences and proposes a new convergence problem setting focusing on subsets (generalized octahedra) rather than all space elements.
The main goal of this paper is twofold. First, we extend some results known in the case of weak greedy algorithms with a scalar parameter to the case of weak greedy algorithms with a weakness sequence. Second, we formulate a new setting of the problem of convergence of greedy algorithms. Usually, we are interested in convergence of an algorithm for all elements of the space. We suggest to study convergence of an algorithm for a subset, which is a generalized octahedron associated with a given dictionary.