Gradient neural dynamics for linear matrix equations and their applications

Marko D. Petković, Marko Kostadinov and Jelena Dakić

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 249, issue C, 560-582

Abstract: Two novel gradient neural dynamics are developed: one for solving a system of two linear matrix equations of the form AXB=C,DXE=F, and another for the matrix equation ∑i=1nAiXBi=C. Convergence properties of the proposed models are analyzed, showing that both models converge globally and exponentially. The analysis is performed in the most general setting of arbitrary (possibly singular) design matrices. The models are applied to the computation of several types of generalized inverses arising from the (B,C)-inverse (Moore–Penrose inverse, Drazin inverse and inverse along the element). Numerical examples (of smaller and larger matrix sizes) are provided to demonstrate the convergence and the validity of the proposed models.

Keywords: Gradient neural network; Linear matrix equation; Drazin inverse; (B,C)-inverse; Moore–Penrose inverse (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:249:y:2026:i:c:p:560-582

DOI: 10.1016/j.matcom.2026.05.031

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