Özaktaş, Hakan2016-01-082016-01-081998http://hdl.handle.net/11693/18555Ankara : 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.xi, 94 leavesEnglishinfo:eu-repo/semantics/openAccessLinear feasibilityregularization of ill conditioned problemstomographyimage reconstruction from projectionsimage restorationimage recoverydescent directionsanalytic centerscentral cutting (localization) methodssubgradient methodssequential and parallel algorithmslong-step methodsconstraints and block projectionssurrogateCimmino’s methodthe relaxation (successive orthogonal projections) methodprojection methodsconvex feasibilityT57.74 .O93 1998Linear programming.Convex programming.Relaxation methods (Mathematics).Thesis