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Andrea Bressan, Michael S Floater, Espen Sande, On best constants in L2 approximation, IMA Journal of Numerical Analysis, Volume 41, Issue 4, October 2021, Pages 2830–2840, https://doi.org/10.1093/imanum/draa041
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Abstract
In this paper we provide explicit upper and lower bounds on certain |$L^2$||$n$|-widths, i.e., best constants in |$L^2$| approximation. We further describe a numerical method to compute these |$n$|-widths approximately and prove that this method is superconvergent. Based on our numerical results we formulate a conjecture on the asymptotic behaviour of the |$n$|-widths. Finally, we describe how the numerical method can be used to compute the breakpoints of the optimal spline spaces of Melkman and Micchelli, which have recently received renewed attention in the field of isogeometric analysis.