A natural gradient descent algorithm for the solution of discrete algebraic Lyapunov equations based on the geodesic distance

Xiaomin Duan, Huafei Sun, Linyu Peng, Xinyu Zhao

研究成果: Article査読

15 被引用数 (Scopus)

抄録

A new framework to calculate the numerical solution of the discrete algebraic Lyapunov equation is proposed by using the geometric structures on the Riemannian manifold. Specifically, two algorithms based on the manifold of positive definite symmetric matrices are provided. One is a gradient descent algorithm with an objective function of the classical Euclidean distance. The other is a natural gradient descent algorithm with an objective function of the geodesic distance on the curved Riemannian manifold. Furthermore, these two algorithms are compared with a traditional iteration method. Simulation examples show that the convergence speed of the natural gradient descent algorithm is the fastest one among three algorithms.

本文言語English
ページ(範囲)9899-9905
ページ数7
ジャーナルApplied Mathematics and Computation
219
19
DOI
出版ステータスPublished - 2013
外部発表はい

ASJC Scopus subject areas

  • 計算数学
  • 応用数学

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