Year: 2014
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 2 : pp. 193–213
Abstract
We present generalized and unified families of $(2n)$-point and $(2n-1)$-point $p$-ary interpolating subdivision schemes originated from Lagrange polynomial for any integers $n ≥ 2$ and $p ≥ 3$. Almost all existing even-point and odd-point interpolating schemes of lower and higher arity belong to this family of schemes. We also present tensor product version of generalized and unified families of schemes. Moreover, error bounds between limit curves and control polygons of schemes are also calculated. It has been observed that error bounds decrease when complexity of the scheme decrease and vice versa. Furthermore, error bounds decrease with the increase of arity of the schemes. We also observe that in general the continuity of interpolating scheme do not increase by increasing complexity and arity of the scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2014.1313nm
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 2 : pp. 193–213
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Interpolating subdivision scheme even-ary schemes odd-ary schemes Lagrange polynomial parameters error bounds tensor product.
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