REAL INTERPOLATION POINTS IN MODEL REDUCTION: JUSTIFICATION, TWO SCHEMES AND AN ERROR BOUND

摘要

A new mathematical justification for using real interpolation points in model reduction is given, with the help of optimal time function approximations by transformed Legendre polynomials. Based on that, two reduction schemes are proposed: The first one applies a projection to the original model and matches 2q moments, similar to known rational Krylov methods. The second one matches q moments while preserving stability and ensuring an optimal approximation of the step response in a weighted L2 norm sense. This new method also provides an error bound.