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Gradient adaptive parameter method for coupled matrix equations with applications in transient heat conduction problem and image steganography
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DOI：10.1016/j.amc.2026.130226.png)
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Abstract
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In the realm of engineering, one frequently encounters coupled linear matrix equations. In this work, based on the study in [1] a new gradient-based parameter free iterative scheme is presented to find solutions for a coupled matrix equations. The proposed iterative method has been proven to attain solutions for the general coupled matrix equations, regardless of the initial matrices. In the following some applications for generalized Sylvester matrix equation such as solving transient heat conduction problem by moving least squares (MLS) scheme as trial approximation in time and space and a new novel transform domain steganography technique-hiding an image message in a high order vector are studied. Lastly, computational experiments are presented to illustrate that the introduced iterative algorithm with optimal parameter selection outperforms the gradient-based iterative scheme in terms of speed, number of iterates, and elapsed times.
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