On inhomogeneous eigenvalue problems. I (Q1091756)

The technique used to obtain asymptotic estimates of solutions of the linear differential system \(\dot u=L(t)u+g\) is based on a generalized kinematic similarity transformation (Lyapunov transformation), which decouples the system. The asymptotic stability properties can be expressed in terms of the largest kinematic eigenvalue \(\lambda\) with corresponding vector z. Some numerical methods are given for the practical computation of \(\lambda\) transforming the problem into an algebraic one by discretizing the derivative: \(\mu x=Ax-b\), where A is a matrix related with L and depending on the particular discretization, \(\mu\) and x approximate \(\lambda\) and z, respectively (\(\mu\) is called the inhomogeneous eigenvalue). The methods are based on shifted power iteration.