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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/893414 |
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| _version_ | 1832565521688559616 |
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| author | Ghulam Mustafa Robina Bashir |
| author_facet | Ghulam Mustafa Robina Bashir |
| author_sort | Ghulam Mustafa |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-a089e30356314038845ad0b1e4a460de |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a089e30356314038845ad0b1e4a460de2025-02-03T01:07:25ZengWileyInternational 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 |
| spellingShingle | Ghulam Mustafa Robina Bashir Four-Point n-Ary Interpolating Subdivision Schemes International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Four-Point n-Ary Interpolating Subdivision Schemes |
| title_sort | four point n ary interpolating subdivision schemes |
| url | http://dx.doi.org/10.1155/2013/893414 |
| work_keys_str_mv | AT ghulammustafa fourpointnaryinterpolatingsubdivisionschemes AT robinabashir fourpointnaryinterpolatingsubdivisionschemes |