On the stability of the $L^{2}$ projection and the quasiinterpolant in the space of smooth periodic splines
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 unifo...
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| creator | Dougalis, D. C. Antonopoulos V. A |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2106.09060 |
| format | Article |
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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
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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
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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.</abstract><doi>10.48550/arxiv.2106.09060</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | On the stability of the $L^{2}$ projection and the quasiinterpolant in the space of smooth periodic splines |
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