Numerical methods for spectral problems: theory and applications
An accelerated technique for solving one type of continuous-time algebraic Riccati equations arising from palindromic eigenvalue problems
*Chun-Yueh Chiang (Center for General Education, National Formosa University)
Matthew M. Lin (Department of Mathematics, National Cheng Kung University)
In recent two decades, palindromic eigenvalue problems (PEP) have great relevance in
control applications associated with the continuous-time descriptor systems and the vibration of fast
trains. In this talk, we investigate the an accelerated technique for solving an eigenpair of PEP.
Our contribution is twofold. First, we introduce a method to transform the eigenpair of linear PEP into a solution of a kind of algebraic Riccati equations (ARE). Second,
we propose an accelerated iteration to obtain a solution of ARE with high order convergence.
We point out that traditional approaches for finding a numerical solution of a nonlinear equation are based on the fixed-point iteration, and the speed of
the convergence is usually linear. With our method, once the existence of ``semigroup property''. holds for a given iteration, It can immediately construct an iterative method which can converge to the solution with the speed of convergence of any desired order.