This paper presents a new method for the analysis of convergence and smoothness of univariate nonuniform subdivision schemes. The analysis involves ideas from the theory of asymptotically equivalent subdivision schemes and nonuniform Laurent polynomial representation together with a new perturbation result. Application of the new method is presented for the analysis of interpolatory subdivision schemes based upon extended Chebyshev systems and for a class of smoothly varying schemes.
Bibliographical noteFunding Information:
This work was supported by Basic Science Research Program 2012R1A1A2004518 and Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology
© 2014, Springer Science+Business Media New York.
- Asymptotic equivalence
- Extended Chebyshev system
- Laurent polynomial
- Nonuniform subdivision
- Smoothly varying scheme