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- Title
On best constants in L2 approximation.
- Authors
Bressan, Andrea; Floater, Michael S; Sande, Espen
- 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.
- Subjects
SUPERCONVERGENT methods; ISOGEOMETRIC analysis; SPLINES; LOGICAL prediction
- Publication
IMA Journal of Numerical Analysis, 2021, Vol 41, Issue 4, p2830
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/draa041