 The exponential convergence rate of Kaczmarz’s algorithm and an acceleration strategy for ARTMengyao Gao, Xuelin Zhang and Guodong Han Applied Mathematics and Computation, 2022, vol. 420, issue C Abstract: Kaczmarz’s algorithm is an iterative method for solving linear system. Generally, its convergence is considered slow. In the first part of this work, the convergence rates of Kaczmarz’s algorithm with a given default order and a random order are studied by using the abstract theorems for the convergence rate of linear operator sequences. It is proved that Kaczmarz’s algorithm always converges exponentially in both cases of the selected order, which is quite different from the slow behavior in practice, such as in image reconstruction. That means there is a remarkable gap between the theoretical rate and the actual rate. The second part of this work is to propose a new scheme with the reordered rays in each view to accelerate the practical Kaczmarz’s algorithm, i.e., the algebraic reconstruction technique (ART) in image reconstruction. Numerical experiments show that our acceleration scheme has a better performance than the previous multilevel and random-order schemes in literature. Keywords: Kaczmarz’s algorithm; Exponential convergence rate; Acceleration of ART (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:420:y:2022:i:c:s0096300321009681 DOI: 10.1016/j.amc.2021.126885 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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