Two-sided Arnoldi and nonsymmetric Lanczos algorithms

We introduce new two-sided Arnoldi recursions and use them to de ne a model reduction procedure for large, linear, time-invariant, multi-input/multi-output differential algebraic systems. We prove that this procedure has desirable moment matching properties. We de ne a corresponding model reduction procedure which is based on a band nonsymmetric Lanczos recursion and prove that if the deflation is exact and there are no breakdowns in the recursions, then these two model reduction procedures generate identical reduced-order systems. We prove similar equivalences for corresponding eigenelement procedures. We concentrate on the theoretical properties of the new algorithms.