Calculating Finite-Dimensional Approximations of Infinite-Dimensional Linear Systems

We consider calculating finite-dimensional approximations of a class of infinite-dimensional linear systems via modal approximation. An H¿ error bound for modal approximation is derived and an inverse power method for finding eigenvalues and eigenfunctions of linear operators arising from distributed parameter linear systems is developed. The inverse power algorithm applies to systems that do not have closed-form eigenvalues and eigenfunctions. The error bound and inverse power method are applied to a heat equation system with spatially varying parameters in order to compute a finite-dimensional transfer function and associated H¿ error bound.