Volume 7, Issue 2
Generalized and Unified Families of Interpolating Subdivision Schemes

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 193-213.

Published online: 2014-07

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• 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.

65D17, 65D07, 65D05

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@Article{NMTMA-7-193, author = {}, title = {Generalized and Unified Families of Interpolating Subdivision Schemes}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1313nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5871.html} }
TY - JOUR T1 - Generalized and Unified Families of Interpolating Subdivision Schemes JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 193 EP - 213 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.1313nm UR - https://global-sci.org/intro/article_detail/nmtma/5871.html KW - Interpolating subdivision scheme, even-ary schemes, odd-ary schemes, Lagrange polynomial, parameters, error bounds, tensor product. AB -

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.

Ghulam Mustafa, Pakeeza Ashraf & Jiansong Deng. (2020). Generalized and Unified Families of Interpolating Subdivision Schemes. Numerical Mathematics: Theory, Methods and Applications. 7 (2). 193-213. doi:10.4208/nmtma.2014.1313nm
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