Two-step parameterized tensor-based iterative methods for solving A_*MX_*MB=C

2025/02/06 by Ratikanta Behera, Behera, Ratikanta, Saroja Kumar Panda +3
Mathematics · Computer Science · #Tensor decomposition and applications #Matrix Theory and Algorithms #Parallel Computing and Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2502.03921

Abstract

Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the tensor equations A_*MX_*MB=C by incorporating preconditioning techniques and parametric optimization to enhance convergence properties. The theoretical results were complemented by comprehensive numerical experiments that demonstrated the computational efficiency of the proposed two-step parametrized iterative methods. The convergence criterion for parameter selection has been studied and a few numerical experiments have been conducted for optimal parameter selection. Effective algorithms were proposed to compute iterative methods based on two-step parameterized tensors, and the results are promising. In addition, we discuss the solution of the Sylvester equations and a regularized least-squares solution for image deblurring problems.

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