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Dynamic sensor selection for biomarker discovery. [PDF]
Pickard J +5 more
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Enhancement of rime algorithm using quadratic interpolation learning for parameters identification of photovoltaic models. [PDF]
Mohamed SA +3 more
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Adaptive Greedy Approximations
Constructive Approximation, 1997Let \({\mathcal H}\) be a Hilbert space. A dictionary \({\mathcal D}\) for \({\mathcal H}\) is a family of unit vectors in \({\mathcal H}\) such that finite linear combinations of \(g_{\gamma }\in {\mathcal D}\) are dense in \({\mathcal H}\). The problem of approximations over a dictionary is studied from different points.
Davis, G., Mallat, S., Avellaneda, M.
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Generalized Approximate Weak Greedy Algorithms
Mathematical Notes, 2005The authors discuss so-called ``generalized approximate weak greedy algorithms'' (gAWGAs) in a Hilbert space, which describe the process of greedy expansions involving errors in calculation of the coefficients in terms of their absolut values. The concepts of ``dictionary'' in a real Hilbert space with inner product and of the ``gAWGA-expansion of an ...
Galatenko, V. V., Livshits, E. D.
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Acta Numerica, 2006
In this survey we discuss properties of specific methods of approximation that belong to a family of greedy approximation methods (greedy algorithms). It is now well understood that we need to study nonlinear sparse representations in order to significantly increase our ability to process (compress, denoise,etc.) large data sets. Sparse representations
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In this survey we discuss properties of specific methods of approximation that belong to a family of greedy approximation methods (greedy algorithms). It is now well understood that we need to study nonlinear sparse representations in order to significantly increase our ability to process (compress, denoise,etc.) large data sets. Sparse representations
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Greedy approximation with regard to non-greedy bases
Advances in Computational Mathematics, 2010The authors present the properties of basis which are important for certain direct and inverse theorems in nonlinear approximation. They study greedy approximation with regard to the basis with different properties. Some results known for unconditional bases are extended to the case of quasi-greedy bases.
Temlyakov, V. N. +2 more
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Two Lower Estimates in Greedy Approximation
Constructive Approximation, 2003Given an arbitrary Hilbert space with a denumerable orthonormal basis, the authors construct two examples providing lower estimates for the rate of convergence of the pure Greedy algorithm and of the weak Greedy algorithm, respectively.
Livshitz, E. D., Temlyakov, V. N.
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Relaxation in Greedy Approximation
Constructive Approximation, 2007We study greedy algorithms in a Banach space from the point of view of convergence and rate of convergence. There are two well-studied approximation methods: the Weak Chebyshev Greedy Algorithm (WCGA) and the Weak Relaxed Greedy Algorithm (WRGA). The WRGA is simpler than the WCGA in the sense of computational complexity.
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Greedy approximation by arbitrary sets
Izvestiya: Mathematics, 2020Abstract We define various algorithms for greedy approximations by elements of an arbitrary set in a Banach space. We study the convergence of these algorithms
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