MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 343-352, 2002

$N$-widths for singularly perturbed problems

Martin Stynes, R. Bruce Kellogg

M. Stynes, Mathematics Department, National University of Ireland, Cork, Ireland, e-mail: m.stynes@ucc.ie; R. B. Kellogg, P. O. Box 698, Landrum, SC 29356, USA, e-mail: kellogg@ipst.umd.edu

Abstract: 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.

Keywords: $N$-width, singularly perturbed, differential equation, boundary value problem, convection-diffusion, reaction-diffusion

Classification (MSC 2000): 41A46, 34E15, 35B25, 65L10, 65N15

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