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

TL;DR

This paper introduces a novel Newton-GADI method for efficiently solving complex continuous-time algebraic Riccati equations by transforming them into Lyapunov equations and analyzing convergence properties.

Contribution

The paper proposes a new Newton-GADI algorithm with an inexact approach and spectral radius analysis for solving Riccati equations more efficiently.

Findings

The Newton-GADI method converges effectively for Riccati equations.

Spectral radius analysis compares convergence rates of Newton-GADI and Newton-ADI.

Numerical tests demonstrate the efficiency of the proposed algorithms.

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.