Controlling semi-convergence phenomenon in non-stationary simultaneous iterative methods

Iranian Journal of Numerical Analysis and Optimization

مقاله 3، دوره 6، شماره 2 - شماره پیاپی 10، آذر 2016، صفحه 51-64   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v6i2.45718

نویسندگان

T. Nikazad^* ؛ M. Karimpour

School of Mathematics, Iran University of Science and Technology, Tehran , Iran.

چکیده

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.

کلیدواژه‌ها

Simultaneous iterative methods؛ Semi-convergence؛ Relaxation parameters؛ Tomographic imaging

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