Convergence-theoretics of classical and krylov waveform relaxation methods for differential-algebraic equations

We present theoretical results on the convergence of iterative methods for the solution of linear differentialalgebraic equations arising from circuit simulation. The iterative methods considered include the continuous-time and discretetime waveform relaxation methods and the Krylov subspace methods in function space. The waveform generalized minimal residual method for solving linear differential-algebraic equations in function space is developed, which is one of the waveform Krylov subspace methods. Some new criteria for convergence of these iterative methods are derived. Examples are given to verify the convergence conditions.