Spectral theory of the linear-quadratic optimal control problem: A new algorithm for spectral computations

In a new formulation of the discrete-time linear-quadratic optimal control problem, the spectrum of a bounded self-adjoint Hilbert space operator, which can be decomposed as the sum of a Toeplitz operator and a compact perturbation, has been shown to elucidate the underlying structure of the problem. A new and efficient algorithm for computing this spectrum is presented.