Bernstein–Walsh type inequalities in unbounded regions with piecewise asymptotically conformal curve in the weighted Lebesgue space

A Piecewise Constant Algorithm for Weighted L1 Approximation over Bounded or Unbounded Regions in R

Using Smolyak’s construction [5], we derive a new algorithm for approximating multivariate functions over bounded or unbounded regions in R with the error measured in a weighted L1-norm. We provide upper bounds for the algorithm’s cost and error for a class of functions whose mixed first order partial derivatives are bounded in L1-norm. In particular, we prove that the error and the cost (measu...

the past hospitalization and its association with suicide attempts and ideation in patients with mdd and comparison with bmd (depressed type) group

چکیده ندارد.

Lebesgue-type Inequalities for Quasi-greedy Bases

We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N term error of approximation times a function of N which depends on the democracy functions and the quasi-greedy constant of the basis. If the basis is democratic this function is bounded by C logN . We show with two examples that this bound is a...

On Lebesgue-type inequalities for greedy approximation

We study the efficiency of greedy algorithms with regard to redundant dictionaries in Hilbert spaces. We obtain upper estimates for the errors of the Pure GreedyAlgorithm and the Orthogonal GreedyAlgorithm in terms of the best m-term approximations. We call such estimates the Lebesgue-type inequalities. We prove the Lebesgue-type inequalities for dictionaries with special structure. We assume t...

Lebesgue-type Inequalities for Quasi-greedy Bases