Discrete Convolution

1
Discrete Convolution
The generating function of ak is defined as
A(z)Sk ak zk
2
Generating Function
Invariance under Affine
Transformations
3
Subdivision and Generating Functions
4
The 4-point scheme Dyn, Gregory, Levin 1987
5
Convergence of Subdivision
Uniform convergence
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Proof of the Theorem
Let Sa be a subdivision rule and S1 be the
subdivision rule for B-splines of degree1. Then
7
Difference Scheme
8
Analysis of 4 point scheme