论文信息 - Nonlinear Approximation in Finite-Dimensional Spaces

Nonlinear Approximation in Finite-Dimensional Spaces

Nonlinear approximation is utilized in many numerical algorithms. In this paper, we shall consider certain problems of nonlinear approximation which arise in image processing. This includes approximation using m terms from a dictionary of functions and greedy algorithms for approximation from such a dictionary. Let X be a Banach space and let ⊂ X be a subset of X whose linear span is dense in X. We shall call such a set a dictionary. Let 6m( ) be the set of all functions g ∈ X such that g is a linear combination of at most m elements of . For f ∈ X, we introduce the error of m-term approximation,

Ronald A. DeVore | Vladimir N. Temlyakov | R. DeVore | V. Temlyakov

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