Greedy-type approximation in Banach spaces and applications (Q1772235)

This paper is based on the author's paper [Adv. Comput. Math. 14, No. 3, 277--292 (2001; Zbl 0988.41022)], where two greedy-type approximations methods, the Weak Chebyshev Greedy Algorithm (WCGA) and the Weak Relaxed Greedy Algorithm (WRGA), have been introduced. Here modifications of the WCGA and WRGA that are motivated by numerical applications are studied. The author develops the theory of the Approximate Weak Chebyshev Greedy Algorithm (AWCGA) and the Approximate Weak Relaxed Greedy Algorithm (AWRGA) in general uniformly smooth Banach spaces. He also gives two applications of greedy type algorithms: (i) A constructive method for \(m\)-term trigonometric approximation in the uniform norm is obtained; (ii) A deterministic sets of points with small \(L_{p}\) discrepancy and with small symmetrized \(L_{p}\) discrepancy are constructed.