Weak thresholding greedy algorithms in Banach spaces

Weak Thresholding Greedy Algorithms in Banach Spaces

We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives the best n-term approximation up to a multiplicative constant, then the system is already “greedy”....

Greedy Algorithms for Reduced Bases in Banach Spaces∗

Given a Banach space X and one of its compact sets F , we consider the problem of finding a good n dimensional space Xn ⊂ X which can be used to approximate the elements of F . The best possible error we can achieve for such an approximation is given by the Kolmogorov width dn(F)X . However, finding the space which gives this performance is typically numerically intractable. Recently, a new gre...

Greedy expansions in Banach spaces

Weak Interpolation in Banach Spaces

Simultaneous 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...