A reduced Newton method for constrained linear least-squares problems

Benedetta MORINI*, Margherita PORCELLI, Raymond H. CHAN

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

34 Citations (Scopus)


We propose an iterative method that solves constrained linear least-squares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally quadratic convergent. Applications to image deblurring problems show that our method gives better restored images than those obtained by projecting or scaling the solution into the dynamic range.

Original languageEnglish
Pages (from-to)2200-2212
Number of pages13
JournalJournal of Computational and Applied Mathematics
Issue number9
Early online date9 Oct 2009
Publication statusPublished - 1 Mar 2010
Externally publishedYes


  • Active set strategy
  • Bound-constrained linear least-squares problems
  • Image processing
  • Newton method


Dive into the research topics of 'A reduced Newton method for constrained linear least-squares problems'. Together they form a unique fingerprint.

Cite this