Riemannian Gradient Algorithm for the Numerical Solution of Linear Matrix Equations
Joint Authors
Zhao, Xinyu
Sun, Huafei
Duan, Xiaomin
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-06
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
A Riemannian gradient algorithm based on geometric structures of a manifold consisting of all positive definite matrices is proposed to calculate the numerical solution of the linear matrix equation Q=X+∑i=1mAiTXAi.
In this algorithm, the geodesic distance on the curved Riemannian manifold is taken as an objective function and the geodesic curve is treated as the convergence path.
Also the optimal variable step sizes corresponding to the minimum value of the objective function are provided in order to improve the convergence speed.
Furthermore, the convergence speed of the Riemannian gradient algorithm is compared with that of the traditional conjugate gradient method in two simulation examples.
It is found that the convergence speed of the provided algorithm is faster than that of the conjugate gradient method.
American Psychological Association (APA)
Duan, Xiaomin& Sun, Huafei& Zhao, Xinyu. 2014. Riemannian Gradient Algorithm for the Numerical Solution of Linear Matrix Equations. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-477119
Modern Language Association (MLA)
Duan, Xiaomin…[et al.]. Riemannian Gradient Algorithm for the Numerical Solution of Linear Matrix Equations. Journal of Applied Mathematics No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-477119
American Medical Association (AMA)
Duan, Xiaomin& Sun, Huafei& Zhao, Xinyu. Riemannian Gradient Algorithm for the Numerical Solution of Linear Matrix Equations. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-477119
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-477119