TY - JOUR
T1 - A New Method for the Analysis of Univariate Nonuniform Subdivision Schemes
AU - Dyn, Nira
AU - Levin, David
AU - Yoon, Jungho
N1 - Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2014/10
Y1 - 2014/10
N2 - 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.
AB - 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.
KW - Asymptotic equivalence
KW - Extended Chebyshev system
KW - Laurent polynomial
KW - Nonuniform subdivision
KW - Smoothly varying scheme
UR - http://www.scopus.com/inward/record.url?scp=84939871952&partnerID=8YFLogxK
U2 - 10.1007/s00365-014-9247-1
DO - 10.1007/s00365-014-9247-1
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AN - SCOPUS:84939871952
SN - 0176-4276
VL - 40
SP - 173
EP - 188
JO - Constructive Approximation
JF - Constructive Approximation
IS - 2
ER -