We analyze and discuss matrix-free and limited memory preconditioners for sparse symmetric positive definite systems and normal equations of large and sparse least-squares problems. The preconditioners are based on a partial Cholesky factorization and can be coupled with a deflation strategy. The construction of the preconditioners requires only matrix-vector products, is breakdown-free, and does not need to form the matrix. The memory requirements of the preconditioners are defined in advance, and they do not depend on the number of nonzero entries in the matrix. When eigenvalue deflation is used, the preconditioners turn out to be suitable for solving sequences of slowly changing systems or linear systems with different right-hand sides. Numerical results are provided, including the case of sequences arising in nonnegative linear least-squares problems solved by interior point methods.

A matrix-free preconditioner for sparse symmetric positive definite systems and least-squares problems / S. Bellavia; J. Gondzio; B. Morini. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - STAMPA. - 35:(2013), pp. A192-A211. [10.1137/110840819]

A matrix-free preconditioner for sparse symmetric positive definite systems and least-squares problems

BELLAVIA, STEFANIA;MORINI, BENEDETTA
2013

Abstract

We analyze and discuss matrix-free and limited memory preconditioners for sparse symmetric positive definite systems and normal equations of large and sparse least-squares problems. The preconditioners are based on a partial Cholesky factorization and can be coupled with a deflation strategy. The construction of the preconditioners requires only matrix-vector products, is breakdown-free, and does not need to form the matrix. The memory requirements of the preconditioners are defined in advance, and they do not depend on the number of nonzero entries in the matrix. When eigenvalue deflation is used, the preconditioners turn out to be suitable for solving sequences of slowly changing systems or linear systems with different right-hand sides. Numerical results are provided, including the case of sequences arising in nonnegative linear least-squares problems solved by interior point methods.
2013
35
A192
A211
S. Bellavia; J. Gondzio; B. Morini
File in questo prodotto:
File Dimensione Formato  
SISC_GONDZIO.pdf

Accesso chiuso

Tipologia: Pdf editoriale (Version of record)
Licenza: Tutti i diritti riservati
Dimensione 249.62 kB
Formato Adobe PDF
249.62 kB Adobe PDF   Richiedi una copia

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

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/763925
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 26
  • ???jsp.display-item.citation.isi??? 22
social impact