Cobos Díaz, FernandoKruglyak, Natan2023-06-202023-06-202011Cobos Díaz, F. & Kruglyak, N. «Exact Minimizer for the Couple ( L ∞ , B V ) and the One-Dimensional Analogue of the Rudin–Osher–Fatemi Model». Journal of Approximation Theory, vol. 163, n.o 4, abril de 2011, pp. 481-90. DOI.org (Crossref), https://doi.org/10.1016/j.jat.2010.11.003.0021-904510.1016/j.jat.2010.11.003https://hdl.handle.net/20.500.14352/42122We provide a simple algorithm that constructs an exact minimizer for the E-functional E(t, f ; L∞, BV) = inf ‖g‖L∞≤t ‖ f − g‖BV . Here L∞, BV stand for the space of bounded functions and the space of functions with bounded variation on the interval [a, b], respectively. As a corollary we obtain the following formula for the K-functional K(N, f ; BV, L∞) v sup a≤x0≤···≤xN≤b −N i=1 | f (xi ) − f (xi+1)|. We also discussed the connection between the results and the Rudin–Osher–Fatemi denoising model.engjournal articlehttps//doi.org/10.1016/j.jat.2010.11.003http://www.sciencedirect.com/science/article/pii/S0021904510002030restricted access517Exact minimizerE-functionalK-functionalRudin-Osher-Fatemi modelL-2MathematicsAnálisis matemático1202 Análisis y Análisis Funcional