Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm

被引:0
作者
Adisorn Kittisopaporn
Pattrawut Chansangiam
机构
[1] King Mongkut’s Institute of Technology Ladkrabang,Department of Mathematics, Faculty of Science
来源
Advances in Difference Equations | / 2021卷
关键词
Generalized Sylvester-transpose matrix equation; Gradient descent; Iterative method; Least-squares solution; 15A60; 15A69; 26B25; 65F45;
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摘要
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.
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