چكيده به لاتين
The superiorization methodology, which is a recently-developed heuristic approach and by taking an iterative algorithm and investigating its perturbation resilience, the algorithm will lead to an acceptable solution. Perturbation resilient in the sense that, even if certain kinds of changes are made at the end of each iteration step,changes occur in ittreation vector, the algorithm keeps still its convergence and and applies these changes in order to achieve an acceptable solution.
In this thesis, 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 iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least-squares solution.
Also in this thesis the superiorization approach that has the convergence speed higher than the previous approach is employed and we have shown the effectiveness of this method with the help of a few examples in the field of image reconstruction.
Keywords: Superurization methodology, Perturbation resilient , block iterative projection methods , image reconstruction
