Four-Point n-Ary Interpolating Subdivision Schemes

Four-Point n-Ary Interpolating Subdivision Schemes

We present an efficient and simple algorithm to generate 4-point n-ary interpolating schemes. Our algorithm is based on three simple steps: second divided differences, determination of position of vertices by using second divided differences, and computation of new vertices. It is observed that 4-po...

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Main Authors: Ghulam Mustafa, Robina Bashir
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2013/893414
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spelling doaj-a089e30356314038845ad0b1e4a460de2020-11-24T23:31:57ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/893414893414Four-Point n-Ary Interpolating Subdivision SchemesGhulam Mustafa0Robina Bashir1Department of Mathematics, The Islamia University of Bahawalpur, Punjab, Bahawalpur 63100, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Punjab, Bahawalpur 63100, PakistanWe present an efficient and simple algorithm to generate 4-point n-ary interpolating schemes. Our algorithm is based on three simple steps: second divided differences, determination of position of vertices by using second divided differences, and computation of new vertices. It is observed that 4-point n-ary interpolating schemes generated by completely different frameworks (i.e., Lagrange interpolant and wavelet theory) can also be generated by the proposed algorithm. Furthermore, we have discussed continuity, Hölder regularity, degree of polynomial generation, polynomial reproduction, and approximation order of the schemes.http://dx.doi.org/10.1155/2013/893414
collection DOAJ
language English
format Article
sources DOAJ
author Ghulam Mustafa
Robina Bashir
spellingShingle Ghulam Mustafa
Robina Bashir
Four-Point n-Ary Interpolating Subdivision Schemes
International Journal of Mathematics and Mathematical Sciences
author_facet Ghulam Mustafa
Robina Bashir
author_sort Ghulam Mustafa
title Four-Point n-Ary Interpolating Subdivision Schemes
title_short Four-Point n-Ary Interpolating Subdivision Schemes
title_full Four-Point n-Ary Interpolating Subdivision Schemes
title_fullStr Four-Point n-Ary Interpolating Subdivision Schemes
title_full_unstemmed Four-Point n-Ary Interpolating Subdivision Schemes
title_sort four-point n-ary interpolating subdivision schemes
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2013-01-01
description We present an efficient and simple algorithm to generate 4-point n-ary interpolating schemes. Our algorithm is based on three simple steps: second divided differences, determination of position of vertices by using second divided differences, and computation of new vertices. It is observed that 4-point n-ary interpolating schemes generated by completely different frameworks (i.e., Lagrange interpolant and wavelet theory) can also be generated by the proposed algorithm. Furthermore, we have discussed continuity, Hölder regularity, degree of polynomial generation, polynomial reproduction, and approximation order of the schemes.
url http://dx.doi.org/10.1155/2013/893414
work_keys_str_mv AT ghulammustafa fourpointnaryinterpolatingsubdivisionschemes
AT robinabashir fourpointnaryinterpolatingsubdivisionschemes
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