Treffer: Displacement Structure: Theory and Applications: Displacement structure: Theory and applications

Title:
Displacement Structure: Theory and Applications: Displacement structure: Theory and applications
Authors:
Thomas Kailath, Ali H. Sayed
Source:
SIAM Review. 37:297-386
Publisher Information:
Society for Industrial & Applied Mathematics (SIAM), 1995.
Publication Year:
1995
Subject Terms:
matrices with displacement structure, structured matrices, 02 engineering and technology, Blaschke products, etc, Direct numerical methods for linear systems and matrix inversion, Moment problems and interpolation problems in the complex plane, state-space models, 01 natural sciences, Factorization of matrices, Discrete-time control/observation systems, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), adaptive filtering, 0202 electrical engineering, electronic engineering, information engineering, time-variant structures, 0101 mathematics, Linear operator methods in interpolation, moment and extension problems, Linear equations (linear algebraic aspects), Model systems in control theory, triangular matrix factorization, interpolation, Filtering in stochastic control theory, General systems theory, Least squares and related methods for stochastic control systems, generalized Schur algorithm, fast computational algorithms, Kalman filtering, Signal detection and filtering (aspects of stochastic processes)
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1095-7200
0036-1445
DOI:
10.1137/1037082
Access URL:
https://zbmath.org/822806
https://doi.org/10.1137/1037082
Accession Number:
edsair.doi.dedup.....adb89ea5e11d1faca949a5d58da154cc
Database:
OpenAIRE

Weitere Informationen

This is a survey of describing how two strands of work from matrix and function theory have come together in interesting ways in some work on fast computational algorithms for matrices with so-called displacement structure. First, the paper reviews some earlier results on matrices with displacement structure and highlights connection with the classical algorithm of Schur and with inverse scattering problems. Then it introduces several generalizations of the notion of displacement structure and some important examples. A hierarchy of generalized Schur algorithms is derived and exhibited in several different forms. Connections with lossless systems, embedding relations, and transmission zeros are highlighted and shown to be relevant to the solution of interpolation problems. Generalized Schur algorithms are then studied in the presence of state-space structure, with immediate applications to problems in state-space estimation and adaptive filtering. Finally, it concludes with a brief account of extensions of the notion of displacement structure to time-variant matrices and with even briefer remarks on other results, applications, and some open problems.