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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |