Simple regularity criteria for subdivision schemes
SIAM Journal on Mathematical Analysis
Multivariate refinement equations and convergence of subdivision schemes
SIAM Journal on Mathematical Analysis
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
Polynomial generation and quasi-interlpolation in stationary non-uniform subdivision
Computer Aided Geometric Design
On the support of recursive subdivision
ACM Transactions on Graphics (TOG)
A family of subdivision schemes with cubic precision
Computer Aided Geometric Design
Multivariate refinable functions, differences and ideals - a simple tutorial
Journal of Computational and Applied Mathematics
Polynomial reproduction by symmetric subdivision schemes
Journal of Approximation Theory
Stationary subdivision schemes reproducing polynomials
Computer Aided Geometric Design
Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction
Journal of Computational and Applied Mathematics
Weighted-powerp nonlinear subdivision schemes
Proceedings of the 7th international conference on Curves and Surfaces
Polynomial reproduction of multivariate scalar subdivision schemes
Journal of Computational and Applied Mathematics
On a class of shape-preserving refinable functions with dilation 3
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
In this paper, we study the ability of convergent subdivision schemes to reproduce polynomials in the sense that for initial data, which is sampled from some polynomial function, the scheme yields the same polynomial in the limit. This property is desirable because the reproduction of polynomials up to some degree d implies that a scheme has approximation order d+1. We first show that any convergent, linear, uniform, and stationary subdivision scheme reproduces linear functions with respect to an appropriately chosen parameterization. We then present a simple algebraic condition for polynomial reproduction of higher order. All results are given for subdivision schemes of any arity m=2 and we use them to derive a unified definition of general m-ary pseudo-splines. Our framework also covers non-symmetric schemes and we give an example where the smoothness of the limit functions can be increased by giving up symmetry.