Pseudo-splines are a rich family of functions that allows the user to meet various demands for balancing polynomial reproduction (i.e., approximation power), regularity and support size. Such a family includes, as special members, B-spline functions, universally known for their usefulness in different fields of application. When replacing polynomial reproduction by exponential polynomial reproduction, a new family of functions is obtained. This new family is here constructed and called the family of exponential pseudo-splines. It is the nonstationary counterpart of (polynomial) pseudo-splines and includes exponential B-splines as a special subclass. In this work we provide a computational strategy for deriving the explicit expression of the Laurent polynomial sequence that identifies the family of exponential pseudo-spline nonstationary subdivision schemes. For this family we study its symmetry properties and perform its convergence and regularity analysis. Finally, we also show that the family of primal exponential pseudo-splines fills in the gap between exponential B-splines and interpolatory cardinal functions. This extends the analogous property of primal pseudo-spline stationary subdivision schemes.
Conti, C., Gemignani, L., & Romani, L. (2016). Exponential pseudo-splines: Looking beyond exponential B-splines. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 439(1), 32-56.
|Citazione:||Conti, C., Gemignani, L., & Romani, L. (2016). Exponential pseudo-splines: Looking beyond exponential B-splines. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 439(1), 32-56.|
|Tipo:||Articolo in rivista - Articolo scientifico|
|Carattere della pubblicazione:||Scientifica|
|Presenza di un coautore afferente ad Istituzioni straniere:||No|
|Titolo:||Exponential pseudo-splines: Looking beyond exponential B-splines|
|Autori:||Conti, C; Gemignani, L; Romani, L|
ROMANI, LUCIA (Ultimo)
|Data di pubblicazione:||2016|
|Rivista:||JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.jmaa.2016.02.019|
|Appare nelle tipologie:||01 - Articolo su rivista|