Title :
An Optimization Approach to the Shift Selection Problem in Alternating Direction Implicit Iteration
Author_Institution :
Dept. of Mechanism & Automobile Eng., Beijing Inst. of Technol., Zhuhai, China
Abstract :
The ADI (alternating direction implicit) iteration is an efficient numerical method for solving the large Lyapunov equations. In this paper, we study the selection of shift parameters for the ADI method which involves the solution of min-max problem-ellipse method. Based on a pair of Arnoldi processes, we first obtain the ellipse which contains the spectrum of the coefficient matrix of Lyapunov equation. After converting the min-max problem into the edge of ellipse, we use the Lingo software which can handle enormous numerical problems to solve the parameter selection problem. The numerical experiments show the efficiency of the ADI parameter selection.
Keywords :
Lyapunov methods; iterative methods; matrix algebra; minimax techniques; Arnoldi processes; Lingo software; Lyapunov equations; alternating direction implicit iteration; min-max problem; numerical method; optimization approach; parameter selection problem; shift selection problem; Automotive engineering; Computational modeling; Computer simulation; Control theory; Matrix converters; Minimax techniques; Optimization methods; Riccati equations; Stability analysis; Symmetric matrices; ADI iteration; Lingo; ellipse; minmax problem;
Conference_Titel :
Computer Modeling and Simulation, 2010. ICCMS '10. Second International Conference on
Conference_Location :
Sanya, Hainan
Print_ISBN :
978-1-4244-5642-0
Electronic_ISBN :
978-1-4244-5643-7
DOI :
10.1109/ICCMS.2010.216
