On diagonally relaxed orthogonal projection methods

Yair Censor, Tommy Elfving, Gabor T. Herman, Touraj Nikazad

Research output: Contribution to journalArticlepeer-review


We propose and study a block-iterative projection method for solving linear equations and/or inequalities. The method allows diagonal componentwise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonally relaxed orthogonal projections (DROP). Diagonal relaxation has proven useful in accelerating the initial convergence of simultaneous and block-iterative projection algorithms, but until now it was available only in conjunction with generalized oblique projections in which there is a special relation between the weighting and the oblique projections. DROP has been used by practitioners, and in this paper a contribution to its convergence theory is provided. The mathematical analysis is complemented by some experiments in image reconstruction from projections which illustrate the performance of DROP.

Original languageEnglish
Pages (from-to)473-504
Number of pages32
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - 2007


  • Block iteration
  • Convex feasibility
  • Diagonal relaxation
  • Projection methods
  • Simultaneous algorithms

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'On diagonally relaxed orthogonal projection methods'. Together they form a unique fingerprint.

Cite this