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)
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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)
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.
This paper is concerned with an inverse problem involving a two-phase moving boundary in two dimensional solidification of pure substance. Using a unique continuation result due to Saut and Schcurer we prove a uniqueness result.