Research output: Contribution to journal › Article › peer-review
Splines of Variable Approximation Order and Their Wavelet Decompositions. / Dem’yanovich, Yu K.
In: Journal of Mathematical Sciences (United States), Vol. 244, No. 3, 01.01.2020, p. 401-418.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Splines of Variable Approximation Order and Their Wavelet Decompositions
AU - Dem’yanovich, Yu K.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - We construct spline (finite element) spaces of variable approximation order and find necessary and sufficient conditions for pseudosmoothness of such splines. We study embedding of the spline spaces on embedded subdivisions and construct the corresponding wavelet decompositions. The constructions are based on the approximation relations defined on a cell subdivision of a differentiable manifold under the assumption that the multiplicity of the covering by supports of the coordinate functions is variable, which causes the variable approximation order. The spline spaces possess the adaptive approximation property. The notion of pseudosmoothness lead to new families of embedded spaces.
AB - We construct spline (finite element) spaces of variable approximation order and find necessary and sufficient conditions for pseudosmoothness of such splines. We study embedding of the spline spaces on embedded subdivisions and construct the corresponding wavelet decompositions. The constructions are based on the approximation relations defined on a cell subdivision of a differentiable manifold under the assumption that the multiplicity of the covering by supports of the coordinate functions is variable, which causes the variable approximation order. The spline spaces possess the adaptive approximation property. The notion of pseudosmoothness lead to new families of embedded spaces.
UR - http://www.scopus.com/inward/record.url?scp=85076788730&partnerID=8YFLogxK
U2 - 10.1007/s10958-019-04626-x
DO - 10.1007/s10958-019-04626-x
M3 - Article
AN - SCOPUS:85076788730
VL - 244
SP - 401
EP - 418
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 3
ER -
ID: 53483547