Método de Projeções Ortogonais

The problem treated in this dissertation is to establish boundedness for the iterates of an iterative algorithm in orthogonal projection on a straight line in projections. This problem was analyzed in a paper by Barany et al. in 1994, which found a necessary and suficient condition in the case d = 2, and analyzed further the case d > 2, under some technical conditions. However, this paper uses non-trivial intuitive arguments and its proofs lack suficient rigor. In this dissertation we discuss and strengthen the results of this paper, in order to complete and simplify its proofs