Convergence of the Multiplicative Algebraic Reconstruction Technique for the Inconsistent System of Equations

Thomas Katsekpor ()
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Thomas Katsekpor: University of Ghana

SN Operations Research Forum, 2023, vol. 4, issue 4, 1-18

Abstract: Abstract We prove that the underrelaxed version of the sequence generated by the multiplicative algebraic reconstruction technique (MART) for equalities in the inconsistent case converges to the solution of an optimization problem, as it is the case in the algebraic reconstruction technique (ART), if the relaxation parameters satisfy certain conditions. This method of proof is based on the relationship that exists between the underrelaxed ART and the optimization problem it solves in the inconsistent case. The majorizing function for the simultaneous version of MART (SMART) which could be used to prove its convergence has also been derived.

Keywords: Kullback-Leibler distance; Multiplicative algebraic reconstruction technique; Inconsistent system of equations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s43069-023-00269-6

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