Convergence and Semi-Convergence of a Class of Constrained Block Iterative Methods
نویسندگان
چکیده
In this paper, we analyze the convergence properties of projected non-stationary block iterative methods (P-BIM) aiming to find a constrained solution large linear, usually both noisy and ill-conditioned, systems equations. We split error kth iterate into noise iteration error, consider each separately. The is treated for more general algorithm, also suited solving feasibility problems in Hilbert space. results P-BIM come out as special case. algorithmic step involves projecting onto closed convex sets. When these sets are polyhedral, finite dimension, it shown that algorithm converges linearly. further derive an upper bound P-BIM. Based on bound, suggest new strategy choosing relaxation parameters, which assist speeding up reconstruction process improving quality obtained images. parameters may depend noise. performance suggested by examples taken from field image projections.
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ژورنال
عنوان ژورنال: Numerical Functional Analysis and Optimization
سال: 2021
ISSN: ['1532-2467', '0163-0563']
DOI: https://doi.org/10.1080/01630563.2021.2001822