@Article{NMTMA-7-193,
author = {Ghulam Mustafa, Pakeeza Ashraf and Jiansong Deng},
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 = {<p style="text-align: justify;">We present generalized and unified families &nbsp;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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2014.1313nm},
url = {http://global-sci.org/intro/article_detail/nmtma/5871.html}
}