STRUCTURE-PRESERVING DOUBLING ALGORITHMS THAT AVOID BREAKDOWNS FOR ALGEBRAIC RICCATI-TYPE MATRIX EQUATIONS

Structure-preserving doubling algorithms (SDAs) are efficient algorithms for solving Riccati-type matrix equations. However, breakdowns may occur in SDAs. To remedy this drawback, in this paper, we first introduce Ω-symplectic forms (Ω-SFs), consisting of symplectic matrix pairs with a Hermitian parametric matrix Ω. Based on Ω-SFs, we develop modified SDAs (MSDAs) for solving the associated Riccati-type equations. MSDAs generate sequences of symplectic matrix pairs in Ω-SFs and prevent breakdowns by employing a reasonably selected Hermitian matrix Ω. In practical implementations, we show that the Hermitian matrix Ω in MSDAs can be chosen as a real diagonal matrix that can reduce the computational complexity. The numerical results demonstrate a significant improvement in the accuracy of the solutions by MSDAs.