Optimal Spline Spaces for \(L^2\) n-Width Problems with Boundary Conditions

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Abstract

In this paper we show that, with respect to the \(L^2\) norm, three classes of functions in \(H^r(0,1)\), defined by certain boundary conditions, admit optimal spline spaces of all degrees \(\ge r-1\), and all these spline spaces have uniform knots.

Keywords

n-widths Splines Isogeometric analysis Green’s functions 

Mathematics Subject Classification

Primary: 41A15 47G10 Secondary: 41A44 

Notes

Acknowledgements

We wish to thank the two referees for their careful reading of the manuscript and their valuable comments that helped improve the paper. Espen Sande was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement 339643.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway

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