Learn More
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)
This paper is concerned with the Simultaneous Iterative Reconstruction Technique (SIRT) class of iterative methods for solving inverse problems. Based on a careful analysis of the semi-convergence behavior of these methods, we propose two new techniques to specify the relaxation parameters adaptively during the iterations, so as to control the propagated(More)
We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit(More)
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal(More)
request, provided it is not made publicly available until 12 months after publication. Abstract An algorithm for solving convex feasibility problem for a finite family of convex sets is considered. The acceleration scheme of De Pierro (em Methodos de projeção para a resolução de sistemas gerais de equações algébricas lineares. Thesis which is designed for(More)
The elastography (elasticity imaging) is one of the recent state-of-the-art methods for diagnosis of abnormalities in soft tissue. The idea is based on the computation of the tissue elasticity distribution. This leads to the inverse elasticity problem; in that, displacement field and boundary conditions are known, and elasticity distribution of the tissue(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)