On the best constants in L^2 approximation

09/30/2019

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by   Andrea Bressan, et al.

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In this paper we provide explicit upper and lower bounds on the L^2n-widths, i.e., the 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.