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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.


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

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