Variable s-step CGNR method for solving the matrix equation AXB = C arising in image processing
DOI: https://doi.org/10.3846/mma.2026.23695Abstract
The matrix equation $ {AXB} = {C}$ is widely utilized in signal and image processing. In this paper, we present a variable s-step algorithm based on the CGNR method for solving this matrix equation by employing normalization techniques. This algorithm is subsequently enhanced through the application of s-step and regularization methods. By varying the number of basic matrices involved (denoted as s), both the accuracy and speed of the algorithm are improved. The proposed algorithm effectively computes solutions to the matrix equation, demonstrating superior performance when the problem matrices are symmetric. Finally, we investigate the performance and efficacy of these techniques through several numerical examples.
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matrix equation, CGNR method, variable s-step algorithm, regularization methodHow to Cite
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.