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Title:Krylov Projection Methods for Model Reduction
Author(s):Grimme, Eric James
Doctoral Committee Chair(s):Kyle Gallivan; Paul Van Dooren
Department / Program:Electrical Engineering
Discipline:Electrical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Engineering, Electronics and Electrical
Abstract: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.
Issue Date:1997
Description:212 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.
Other Identifier(s):(MiAaPQ)AAI9737124
Date Available in IDEALS:2015-09-25
Date Deposited:1997

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