Four-Pointn-Ary Interpolating Subdivision Schemes

Abstract

We present an efficient and simple algorithm to generate 4-pointn-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-pointn-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.

A Family of 6-Point n-Ary Interpolating Subdivision Schemes

“…A general formulae was introduced by Muatafa and Rehman [6] to cover (2b+4)-point n-ary interpolation and approximation schemes for every integers b 0 and n2. Mustafa and Bashir [7] proposed a very potential but easy algorithm for producing 4-point n-ary interpolation scheme.…”