مريم بحركاظمي

‎When applying the non-stationary simultaneous iterative methods for‎ ‎solving an ill-posed set of linear equations‎, ‎the error usually initially decreases but after some iterations‎, ‎depending on the amount of noise in the‎ ‎data‎, ‎and the degree of ill-posedness‎, ‎it starts to increase‎. ‎This phenomenon‎ ‎is called semi-convergence‎. ‎We study the semi-convergence behavior of the‎ ‎non-stationary simultaneous iterative methods and obtain an upper bound‎ ‎for data error (noise error)‎. ‎Based on this bound‎, ‎we propose new ways‎ ‎to specify the relaxation parameters to control the semi-convergence‎. ‎The‎ ‎performance of our strategies is shown by examples taken from tomographic‎ ‎imaging‎. Keywords: ‎Simultaneous iterative methods; Semi-convergence; Relaxation‎ ‎parameters; Tomographic imaging.‎