Greedy approximation

By Vladimir N. Temlyakov. Acta Numerica, 2008

422 citations recorded by the source corpus.

Subfields: Education, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0575bfbcacc8874177e182e8e671027d281539ff

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Citations in the corpus

Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces (2011, positive): “Progressive definitions of PGDs can thus be considered as Greedy algorithms [37] for constructing separated representations [1,6].”
Convergence of a greedy algorithm for high-dimensional convex nonlinear problems (2010, methodology): “The method described above has been introduced by Chinesta[1] for solving high-dimensional Fokker-Planck equations, by Nouy[10] in the context of uncertainty quantification in mechanics, and is very much related to so-called greedy algorithms[12, 8] used in nonlinear approximation theory.”
Generalized Sobol sensitivity indices for dependent variables: numerical methods (2013, background): “We particularly focus on the l0 penalty [28] and on the Lasso regression [29].”
Greedy Algorithms for Structurally Constrained High Dimensional Problems (2011, background): “Such rates of convex approximation in non-Hilbert spaces have been studied earlier (see, for example, [10, 11]).”
Lebesgue inequalities for the greedy algorithm in general bases (2016, neutral): “[21, 22] for a detailed presentation and background.”
Lebesgue-Type Inequalities for Quasi-greedy Bases (2011, background): “For a survey on Lebesgue-type inequalities for the greedy algorithm see [18, 19] and the references therein.”
Greedy Approximation of High-Dimensional Ornstein–Uhlenbeck Operators (2011, neutral): “(1) Pure Greedy Algorithm-based approximations such as Algorithm 1 have been proved to obey the slightly improved rate (see [Tem08, Remark 2.3.11] and references therein) (2) In [CEL11, Theorem 4.1] it is shown that the convergence of the Orthogonal Greedy Algorithm is exponentially fast if the…”
Hyperbolic Cross Approximation (2016, methodology): “Keeping this remark in mind we, however, use the term greedy algorithm in this paper because it has been used in previous papers and has become a standard name for procedures alike Weak Chebyshev Greedy Algorithm (see below) and for more general procedures of this type (see for instance [71], [373])”
The Marcinkiewicz-Type Discretization Theorems (2017, methodology): “overing numbers, entropy numbers). Bounds for the entropy numbers of function classes are important by themselves and also have important connections to other fundamental problems (see, for instance, [13], Ch.3 and [3], Ch.6). Another prominent example of a discretization problem is the problem of n”
Projection-Free Optimization on Uniformly Convex Sets (2020, neutral): “For a η ∈ ]0 , 1] , we have O (1 /T 1 /η ) (see for instance (Temlyakov, 2011) or (Nguyen and Petrova, 2017, Lemma 4.2.))”
Results and Questions on a Nonlinear Approximation Approach for Solving High-dimensional Partial Differential Equations (2008, background): “We refer to [2, 3, 10] for some relevant contributions, among many.”
Convergence Rates for Greedy Algorithms in Reduced Basis Methods (2010, neutral): “We emphasize that this greedy algorithm differs from those which aim at approximating one given function f by a finite linear combination of elements from a given dictionnary (see [7] for a complete survey on this type of greedy algorithms).”
Greedy algorithms for high-dimensional non-symmetric linear problems (2012, methodology): “The relaxed versions of the X-Greedy and Dual Greedy algorithms are proved to converge [20] provided that”
Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker-Planck Equation (2012, background): “, [42, 4, 31, 5]) and well-known drawbacks of the canonical decomposition, the efficient use of tensor solvers in this approach will be limited by the accuracy demands and restrictions on the rank parameters.”