Four-Pointn-Ary Interpolating Subdivision Schemes | Zendy

Ghulam Mustafa | Zendy; Robina Bashir | Zendy

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Four-Pointn-Ary Interpolating Subdivision Schemes

Author(s) -

Ghulam Mustafa,

Robina Bashir

Publication year - 2013

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2013/893414

Subject(s) - mathematics , polynomial , lagrange polynomial , simple (philosophy) , degree (music) , algorithm , point (geometry) , order (exchange) , combinatorics , subdivision , position (finance) , discrete mathematics , geometry , mathematical analysis , philosophy , physics , archaeology , epistemology , finance , acoustics , economics , history

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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