The New Method for Computing the Lyapunov Matrix Equations

摘要

The method of CAKI is improved, the method of CAKI is an accelerated iterative method combining the method of KPIM and the Chebyshev acceleration for symmetric Lyapunov matrix equation. In order to reduce the computation cost, the matrix Hessenberg decomposition is given at first, the method of CAKI is used for iterating. The corresponding algorithms and the numerical example are given then. At the same time the computation and store cost are given. Although the store cost is little bigger, the computation cost drops rapidly.