On the partial realization problem
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TLDR
This paper takes a unified approach to the partial realization problem in which it seeks to incorporate ideas from numerical linear algebra, most of which were originally developed in other contexts.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-04-01 and is currently open access. It has received 295 citations till now. The article focuses on the topics: Numerical linear algebra.read more
Citations
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Dissertation
Krylov Projection Methods for Model Reduction
TL;DR: The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation, based on which three algorithms for model reduction are proposed, which are suited for parallel or approximate computations.
A Survey of Model Reduction Methods for Large-Scale Systems
TL;DR: An overview of model reduction methods and a comparison of the resulting algorithms is presented, finding that the approximation error in the former case behaves better globally in frequency while in the latter case the local behavior is better.
Journal ArticleDOI
Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
TL;DR: This paper gives an overview of the recent progress in other Krylov subspace techniques for a variety of dynamical systems, including second-order and nonlinear systems, and case studies arising from circuit simulation, structural dynamics and microelectromechanical systems are presented.
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Iterative solution of linear systems
TL;DR: Recent advances in the field of iterative methods for solving large linear systems are reviewed, focusing on developments in the area of conjugate gradient-type algorithms and Krylov subspace methods for nonHermitian matrices.
References
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Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
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An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
TL;DR: In this article, a systematic method for finding the latent roots and principal axes of a matrix, without reducing the order of the matrix, has been proposed, which is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of minimized iterations.
Book
Algebraic Coding Theory
TL;DR: This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.
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Shift-register synthesis and BCH decoding
TL;DR: It is shown in this paper that the iterative algorithm introduced by Berlekamp for decoding BCH codes actually provides a general solution to the problem of synthesizing the shortest linear feedback shift register capable of generating a prescribed finite sequence of digits.