Controlling Semiconvergence Phenomenon in Nonstationary Simultaneous Iterative Methods

When applying the nonstationary simultaneous iterative methods for solving an illposed 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 illposedness, it starts to increase. this phenomenon is called semiconvergence. we study the semiconvergence behavior of the nonstationary 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 semiconvergence. the performance of our strategies is shown by examples taken from tomographic imaging.