CONVERGENCE-THEORETICS OF CLASSICAL AND KRYLOV WAVE-FORM RELAXATION METHODS FOR DIFFERENTIAL-ALGEBRAIC EQUATIONS

We present theoretical results on the convergence of iterative methods for the solution of linear differential-algebraic equations arising f rom circuit simulation. The iterative methods considered include the c ontinuous-time and discrete-time waveform relaxation methods and the K rylov subspace methods in function space. The waveform generalized min imal residual method for solving linear differential-algebraic equatio ns in function space is developed, which is one of the waveform Krylov subspace methods. Some new criteria for convergence of these iterativ e methods are derived. Examples are given to verify the convergence co nditions.