TABLE OF CONTENTS In this section, we briefly review model order reduction methods based on Krylov subspaces from a historical perspective in the computer-aided design community.
Projection-based model order reduction techniques have been intensively studied in the past two decades [32, 37, 63, 85, 91, 113]. Projection-based methods were pioneered by asymptotic waveform evaluation (AWE) algorithm [91], where explicit moment matching was used to compute dominant poles at low frequency. The Pade via Lanczos (PVL) [32], block PVL (MPVL) [33], symmetric block PVM (SyMPVL) [38], and Arnoldi transformation [113] methods improved the numerical stability of AWE, while the split congruence transformation [63] method and PRIMA [85] can further produce passive models. However, reduced circuit matrices by PRIMA are larger than direct pole marching (having more poles than necessary) [1] and PRIMA does not preserve certain important circuit properties such reciprocity [37]. The latest development by structured projection can preserve reciprocity [37], but it does not realize the reduced circuit matrices. The extension of structure-preserving MOR can be found in Chapter 8 of this book.
