PMTBR: A Family of Approximate Principal-components-like Reduction Algorithms

Abstract

In this chapter we present a family of algorithms that can be considered intermediate between frequency domain projection methods and approximation of truncated balanced realizations. The methods discussed are computationally simple to implement, have good error properties, and possess simple error estimation and order control procedures. By tailoring the method to take into account a statistical representation of individual problem characteristics, more efficient, improved results have been obtained in several situations, meaning models of small order that retain acceptable accuracy, on problems for which many other methods struggle. Examples are shown to illustrate the algorithms in the contexts of frequency weighting, circuit simulation with parasitics networks having large numbers of input/output ports, and interconnect modeling in the presence of parameter change due to process variation.