Generalized Approximate Weak Greedy Algorithms
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We study generalized approximate weak greedy algorithms. The main difference of these algorithms from approximate weak greedy algorithms proposed by R. Gribonval and M. Nielsen consists in that errors in the calculation of the coefficients can be prescribed in terms of not only their relative values, but also their absolute values. We present conditions on the parameters of generalized approximate weak greedy algorithms which are sufficient for the expansions resulting from the use of this algorithm to converge to the expanded element. It is shown that these conditions cannot be essentially weakened. We also study some questions of the convergence of generalized approximate weak greedy expansions with respect to orthonormal systems.
Key wordsgeneralized approximate weak greedy algorithm pure greedy algorithm matching pursuit Hilbert space orthonormal system
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- 3.J. H. Friedman and W. Stueuzle, “Projection pursuit regression,” J. Amer. Statist. Assoc., 76 (1981), 817–823.Google Scholar
- 5.L. K. Jones, “On a conjecture of Huber concerning the convergence of PP-regression,” Ann. Statist., 15 (1987), 880–882.Google Scholar
- 6.L. Jones, “A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and network training,” Ann. Statist., 20 (1992), 608–613.Google Scholar
- 7.L. Rejto and G. G. Walter, “Remarks on projection pursuit regression and density estimation,” Stochastic Anal. Appl., 10 (1992), 213–222.Google Scholar
- 8.E. D. Livshits and V. N. Temlyakov, “On the convergence of weak greedy algorithms,” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 232 (2001), 236–247.Google Scholar
- 9.V. N. Temlyakov, “A criterion for convergence of weak greedy algorithms,” in: Preprint at http://www.math.sc.edu/∼imip/00.html.Google Scholar
- 10.V. V. Galatenko and E. D. Livshitz (Livshits), “On the convergence of approximate weak greedy algorithms,” East J. Approx., 9 (2003), no. 1, 43–49.Google Scholar