1. STRUCTURE-PRESERVING DOUBLING ALGORITHMS THAT AVOID BREAKDOWNS FOR ALGEBRAIC RICCATI-TYPE MATRIX EQUATIONS.
- Author
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TSUNG-MING HUANG, YUEH-CHENG KUO, WEN-WEI LIN, and SHIH-FENG SHIEH
- Subjects
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MATRICES (Mathematics) , *EQUATIONS , *RICCATI equation , *ALGORITHMS , *ALGEBRAIC equations , *COMPUTATIONAL complexity , *HERMITIAN forms - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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