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Kyle Gallivan Paul Van Dooren Grimme, Eric James 2015-09-25T20:09:57Z 2015-09-25T20:09:57Z 10000-01-01 1997 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. Made available in DSpace on 2015-09-25T20:09:57Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9737124.pdf: 9938292 bytes, checksum: e83075456d1562438e39d667f9e269f0 (MD5) Previous issue date: 1997 Embargo set by: Seth Robbins for item 82461 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 212 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997. http://hdl.handle.net/2142/81180 (MiAaPQ)AAI9737124 eng Engineering, Electronics and Electrical Krylov Projection Methods for Model Reduction text Electrical Engineering Electrical Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.