Krylov Projection Methods for Model Reduction

212 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.This dissertation focuses on efficiently forming reduced-order models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reduced-order models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczos-based methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a combination of theory and examples. Independent of the precise algorithm, a host of supporting tools are also developed to form a complete model reduction package. Techniques for choosing the matching frequencies, estimating the modeling error, insuring the model's stability, treating multiple-input multiple-output systems, implementing parallelism, and avoiding a need for exact factors of large matrix pencils are all examined to various degrees.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD