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… (More)
We give a detailed study of the semiconvergence behavior of projected nonsta-tionary simultaneous iterative reconstruction technique (SIRT) algorithms, including the projected Landweber algorithm. We also consider the use of a relaxation parameter strategy, proposed recently for the standard algorithms, for controlling the semiconvergence of the projected… (More)
(Convergence analysis, stopping criteria, and good advice) Goal: use measured data to compute " hidden " information. The forward problem is formulated as a certain transform formulate a stable way to compute the inverse transform. Example: the inverse Radon transform for tomography. Use the forward model to produce a Krylov subspace inversion amounts… (More)
Column-oriented versions of algebraic iterative methods are interesting alternatives to their row-version counterparts: they converge to a least squares solution, and they provide a basis for saving computational work by skipping small updates. In this paper we consider the case of noise-free data. We present a convergence analysis of the column algorithms,… (More)
In this paper, we analyze the semiconvergence behavior of a non-stationary sequential block iterative method. Based on a slightly modified problem, in the form of a regularized problem, we obtain three techniques for picking relaxation parameters to control the propagated noise component of the error. Also, we give the convergence analysis of the iterative… (More)
In our recently published paper, Fig. 3 is unfortunately not quite correct – the three error plots at the bottom are correct, but the top left and middle phantoms are incorrect. The correct phantoms are shown in the above figure.
In this paper we introduce a sequential block iterative method and its simultaneous version with optimal combination of weights (instead of convex combination) for solving convex feasibility problems. When the intersection of the given family of convex sets is nonempty, it is shown that any sequence generated by the given algorithms converges to a feasible… (More)