-

 

 

 




Optimization Online





 

On diagonally-relaxed orthogonal projection methods

Yair Censor (yair***at***math.haifa.ac.il)
Tommy Elfving (toelf***at***mail.mai.liu.se)
Gabor T. Herman (gabortherman***at***yahoo.com)
Touraj Nikazad (tonik***at***mail.mai.liu.se)

Abstract: We propose and study a block-iterative projections method for solving linear equations and/or inequalities. The method allows diagonal component-wise 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 convergence theory is provided. The mathematical analysis is complemented by some experiments in image reconstruction from projections which illustrate the performance of DROP.

Keywords: block-iterations, convex feasibility, diagonal relaxation, projection methods, simultaneous algorithms.

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Applications -- Science and Engineering (Biomedical Applications )

Citation: SIAM Journal on Scientific Computing, Vol. 30 (2008), pp. 473-504.

Download:

Entry Submitted: 01/28/2007
Entry Accepted: 01/28/2007
Entry Last Modified: 04/17/2008

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society