DOI number:10.1016/j.jfranklin.2023.08.022

Journal:Journal of the Franklin Institute

Key Words:General coupled Sylvester matrix equations, generalized conjugate direction algorithm, least squares solution, inner product space

Abstract:In this paper, a generalized conjugate direction algorithm (GCD) is proposed for solving general coupled Sylvester matrix equations. The GCD algorithm is an improved gradient algorithm, which can realize gradient descent by introducing matrices $P_{j}(k)$ and $T_{j}(k)$ to construct parameters $\alpha(k)$ and $\beta(k)$. The matrix $P_{j}(k)$ and $T_{j}(k)$ are iterated in a cross way to accelerate the convergence rate. In addition, it is further proved that the algorithm converges to the exact solution in finite iteration steps in the absence of round-off errors if the system is consistent. Also, the sufficient conditions for least squares solutions and the minimum F-norm solutions are obtained. Finally, numerical examples are given to demonstrate the effectiveness of the GCD algorithm.

First Author:Zijian Zhang

Indexed by:Journal paper

Correspondence Author:Xuesong Chen

Volume:360

Issue:14

Page Number:10409-10432

Translation or Not:no

Date of Publication:2023-09-05

Included Journals:SCI

Links to published journals:https://doi.org/10.1016/j.jfranklin.2023.08.022