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 [10.1016/j.jmaa.2016.02.019].

Exponential pseudo-splines: Looking beyond exponential B-splines

ROMANI, LUCIA
Ultimo
2016

Abstract

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.
Articolo in rivista - Articolo scientifico
Exponential B-spline; Exponential polynomial reproduction; Exponential pseudo-spline; Minimal support; Nonstationary subdivision;
Exponential B-spline; Exponential polynomial reproduction; Exponential pseudo-spline; Minimal support; Nonstationary subdivision
English
2016
439
1
32
56
none
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 [10.1016/j.jmaa.2016.02.019].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/138904
Citazioni
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 19
Social impact