A Natural Gradient Descent Algorithm for the Solution of Lyapunov Equations Based on the Geodesic Distance
Year: 2014
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 1 : pp. 93–106
Abstract
A new framework based on the curved Riemannian manifold is proposed to calculate the numerical solution of the Lyapunov matrix equation by using a natural gradient descent algorithm and taking the geodesic distance as the objective function. Moreover, a gradient descent algorithm based on the classical Euclidean distance is provided to compare with this natural gradient descent algorithm. Furthermore, the behaviors of two proposed algorithms and the conventional modified conjugate gradient algorithm are compared and demonstrated by two simulation examples. By comparison, it is shown that the convergence speed of the natural gradient descent algorithm is faster than both of the gradient descent algorithm and the conventional modified conjugate gradient algorithm in solving the Lyapunov equation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1310-m4225
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 1 : pp. 93–106
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Lyapunov equation Geodesic distance Natural gradient descent algorithm.
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