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arXiv · 2203.02163

A general alternating-direction implicit Newton method for solving complex continuous-time algebraic Riccati matrix equation

Shifeng Li·Kai Jiang Juan Zhang
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Abstract

In this paper, applying the Newton method, we transform the complex continuous-time algebraic Riccati matrix equation into a Lyapunov equation. Then, we introduce an efficient general alternating-direction implicit (GADI) method to solve the Lyapunov equation. The inexact Newton-GADI method is presented to save computational amount effectively. Moreover, we analyze the convergence of the Newton-GADI method. The convergence rate of the Newton-GADI and Newton-ADI methods is compared by analyzing their spectral radii. Furthermore, we give a way to select the quasi-optimal parameter. Corresponding numerical tests are shown to illustrate the effectiveness of the proposed algorithms.

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Shifeng Li, Kai Jiang Juan Zhang. 2022-03-04. A general alternating-direction implicit Newton method for solving complex continuous-time algebraic Riccati matrix equation. https://arxiv.org/abs/2203.02163

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