The one-sided Loewner framework and connections to other model reduction methods based on interpolation

Abstract

We present an extension of the Loewner framework, an established data-driven reduction, and identification method. This will be referred to as the one-sided Loewner framework since only one set of interpolation conditions are explicitly and exactly matched. For the other set of conditions, approximated interpolation is imposed. We describe how to explicitly characterize new interpolation conditions, derived from the latter set. We also show connections to the iterative AAA algorithm. Typical applications include constructing reduced models from frequency response data measured from systems in electronics or mechanical engineering. We illustrate the application of the main method on a large-scale benchmark example.