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Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm
Author(s)
Kittisopaporn, Adisorn
Date Issued
December 1, 2021
Type
Article
Abstract
This paper proposes an effective gradient-descent iterative algorithm for solving a generalized Sylvester-transpose equation with rectangular matrix coefficients. The algorithm is applicable for the equation and its interesting special cases when the associated matrix has full column-rank. The main idea of the algorithm is to have a minimum error at each iteration. The algorithm produces a sequence of approximated solutions converging to either the unique solution, or the unique least-squares solution when the problem has no solution. The convergence analysis points out that the algorithm converges fast for a small condition number of the associated matrix. Numerical examples demonstrate the efficiency and effectiveness of the algorithm compared to renowned and recent iterative methods.
Citation
Advances in Difference Equations, 2021(1), 2021