On diagonally-relaxed orthogonal projection methods
Yair Censor (yairmath.haifa.ac.il)
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
Modify/Update this entry
|Visitors||Authors||More about us||Links|
Search, Browse the Repository
Give us feedback
|Optimization Journals, Sites, Societies|