The expansion in Gegenbauer polynomials: a simple method for the fast computation of the Gegenbauer coefficients (Articolo in rivista)

Type

• Prodotto della ricerca (Classe)
• Articolo in rivista (Classe)

Label

• The expansion in Gegenbauer polynomials: a simple method for the fast computation of the Gegenbauer coefficients (Articolo in rivista) (literal)

Anno

• 2013-01-01T00:00:00+01:00 (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi

• 10.1016/j.jcp.2013.01.008 (literal)

Alternative label

• De Micheli Enrico; Viano Giovanni Alberto (2013)
  The expansion in Gegenbauer polynomials: a simple method for the fast computation of the Gegenbauer coefficients
  in Journal of computational physics (Print)
  (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori

• De Micheli Enrico; Viano Giovanni Alberto (literal)

Pagina inizio

• 112 (literal)

Pagina fine

• 122 (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume

• 239 (literal)

Rivista

• Journal of computational physics (Rivista)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali

• 11 (literal)

Note

• ISI Web of Science (WOS) (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni

• Istituto di Biofisica, Consiglio Nazionale delle Ricerche, Genova, Italy Dipartimento di Fisica, Universita' di Genova, Genova, Italy (literal)

Titolo

• The expansion in Gegenbauer polynomials: a simple method for the fast computation of the Gegenbauer coefficients (literal)

Abstract

• We present a simple and fast algorithm for the computation of the Gegenbauer transform, which is known to be very useful in the development of spectral methods for the numerical solution of ordinary and partial differential equations of physical interest. We prove that the coefficients of the expansion of a function f(x) in Gegenbauer (also known as ultraspherical) polynomials coincide with the Fourier coefficients of a suitable integral transform of the function f(x). This allows to compute N Gegenbauer coefficients in O(N log_2 N) operations by means of a single Fast Fourier Transform of the integral transform of f(x). We also show that the inverse Gegenbauer transform is expressible as the Abel-type transform of a suitable Fourier series. This fact produces a novel algorithm for the fast evaluation of Gegenbauer expansions. (literal)

Prodotto di

• Modelli di Organizzazione e Dinamica di Sistemi Complessi (MD.P01.004.001) (Modulo)
• Istituto di biofisica (IBF) (Istituto)

Autore CNR

• ENRICO DE MICHELI (Persona)

Insieme di parole chiave

• Keywords of "The expansion in Gegenbauer polynomials: a simple method for the fast computation of the Gegenbauer coefficients" (Insieme di parole chiave)

Incoming links:

Prodotto

• Istituto di biofisica (IBF) (Istituto)
• Modelli di Organizzazione e Dinamica di Sistemi Complessi (MD.P01.004.001) (Modulo)

Autore CNR di

• ENRICO DE MICHELI (Persona)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#rivistaDi

• Journal of computational physics (Rivista)

Insieme di parole chiave di

• Keywords of "The expansion in Gegenbauer polynomials: a simple method for the fast computation of the Gegenbauer coefficients" (Insieme di parole chiave)