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

Advances in Difference Equations

article

Kittisopaporn, Adisorn¹  Chansangiam, Pattrawut¹ 

[1] Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang

关键词: Generalized Sylvester-transpose matrix equation;    Gradient descent;    Iterative method;    Least-squares solution;   

DOI  :  10.1186/s13662-021-03427-4

学科分类：航空航天科学

来源: SpringerOpen

【 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.

【 授权许可】

CC BY