Modified Alternately Linearized Implicit Iteration Methods for Nonsymmetric Coupled Algebraic Riccati Equation

Abstract

In this paper, according to the Shamanskii technology, an alternately linearized implicit (ALI) iteration method is proposed to compute the minimal nonnegative solution to the nonsymmetric coupled algebraic Riccati equation. Based on the ALI iteration method, we propose two modified alternately linearized implicit (MALI) iteration methods with double parameters. Further, we prove the monotone convergence of these iteration methods. Numerical examples demonstrate the effectiveness of the presented iteration methods.

Keywords

Nonsymmetric coupled algebraic Riccati equation / Shamanskii technology / Alternately linearized iteration (ALI) method / Monotone convergence / 15A24 / 15A06 / 65F10 / 65F45

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Shanghai University