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\(N\)-widths for singularly perturbed problems. (English) Zbl 1005.41009

Summary: Kolmogorov \(N\)-widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the \(N\)-widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.

MSC:

41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
34E15 Singular perturbations for ordinary differential equations
35B25 Singular perturbations in context of PDEs
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65N15 Error bounds for boundary value problems involving PDEs
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