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

Authors :
TSUNG-MING HUANG
YUEH-CHENG KUO
WEN-WEI LIN
SHIH-FENG SHIEH
Source :
SIAM Journal on Matrix Analysis & Applications; 2024, Vol. 45 Issue 1, p59-83, 25p
Publication Year :
2024

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]

Details

Language :
English
ISSN :
08954798
Volume :
45
Issue :
1
Database :
Complementary Index
Journal :
SIAM Journal on Matrix Analysis & Applications
Publication Type :
Academic Journal
Accession number :
177132686
Full Text :
https://doi.org/10.1137/23M1551791