On the stability of the $L^{2}$ projection and the quasiinterpolant in the space of smooth periodic splines
Abstract
In this paper we derive stability estimates in $L^{2}$- and $L^{\infty}$- based Sobolev spaces for the $L^{2}$ projection and a family of quasiinterolants in the space of smooth, 1-periodic, polynomial splines defined on a uniform mesh in $[0,1]$. As a result of the assumed periodicity and the uniform mesh, cyclic matrix techniques and suitable decay estimates of the elements of the inverse of a Gram matrix associated with the standard basis of the space of splines, are used to establish the stability results.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.09060
- arXiv:
- arXiv:2106.09060
- Bibcode:
- 2021arXiv210609060D
- Keywords:
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- Mathematics - Numerical Analysis;
- 65D07;
- 65M12
- E-Print:
- 13 pages