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Algorithms for linear and convex feasibility problems: A brief study of iterative projection, localization and subgradient methods
Ankara : Department of Industrial Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1998.Thesis (Ph.D.) -- Bilkent University, 1998.Includes bibliographical references leaves 86-93.Several algorithms for the feasibility problem are investigated. For linear systems,
a number of different block projections approaches have been implemented and
compared. The parallel algorithm of Yang and Murty is observed to be much slower
than its sequential counterpart. Modification of the step size has allowed us to
obtain a much better algorithm, exhibiting considerable speedup when compared
to the sequential algorithm. For the convex feasibility problem an approach
combining rectangular cutting planes and subgradients is developed. Theoretical
convergence results are established for both ca^es. Two broad classes of image
recovery problems are formulated as linear feasibility problems and successfully
solved with the algorithms developed.Özaktaş, HakanPh.D