In the solution of ill-posed problems by means of regularization methods, a crucial issue is the computation of the regularization parameter. In this work we focus on the Truncated Singular Value Decomposition (TSVD) and Tikhonov method and we define a method for computing the regularization parameter based on the behavior of Fourier coefficients. We compute a safe index for truncating the TSVD and consequently a value for the regularization parameter of the Tikhonov method. An extensive numerical experimentation is carried out on the Hansen's Regtool test problems and the results confirm the effectiveness and robustness of the method proposed.

Computation of Regularization Parameters using the Fourier Coefficients / F. Zama. - In: JOURNAL OF PURE AND APPLIED MATHEMATICS: ADVANCES AND APPLICATIONS. - ISSN 0974-9381. - STAMPA. - 2:(2009), pp. 145-167.

Computation of Regularization Parameters using the Fourier Coefficients.

ZAMA, FABIANA
2009

Abstract

In the solution of ill-posed problems by means of regularization methods, a crucial issue is the computation of the regularization parameter. In this work we focus on the Truncated Singular Value Decomposition (TSVD) and Tikhonov method and we define a method for computing the regularization parameter based on the behavior of Fourier coefficients. We compute a safe index for truncating the TSVD and consequently a value for the regularization parameter of the Tikhonov method. An extensive numerical experimentation is carried out on the Hansen's Regtool test problems and the results confirm the effectiveness and robustness of the method proposed.
2009
Computation of Regularization Parameters using the Fourier Coefficients / F. Zama. - In: JOURNAL OF PURE AND APPLIED MATHEMATICS: ADVANCES AND APPLICATIONS. - ISSN 0974-9381. - STAMPA. - 2:(2009), pp. 145-167.
F. Zama
File in questo prodotto:
Eventuali allegati, non sono esposti

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/11585/81229
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact