Time-Varying Systems and Computations / Edition 1

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Time-Varying Systems and Computations is a unique book providing a detailed and consistent exposition of a powerful unifying framework (developed by the authors) for the study of time-variant systems and the computational aspects and problems that arise in this context. While complex function theory and linear algebra provide much of the fundamental mathematics needed by engineers engaged in numerical computations, signal processing and/or control, there has long been a large, abstruse gap between the two fields. This book shows the reader how the gap between analysis and linear algebra can be bridged. In a fascinating monograph, the authors explore, discover and exploit many interesting links that exist between classical linear algebraic concepts and complex analysis.
Time-Varying Systems and Computations opens for the reader new and exciting perspectives on linear algebra from the analysis point of view. It clearly explains a framework that allows the extension of classical results, from complex function theory to the case of time-variant operators and even finite-dimensional matrices. These results allow the user to obtain computationally feasible schemes and models for complex and large-scale systems.
Time-Varying Systems and Computations will be of interest to a broad spectrum of researchers and professionals, including applied mathematicians, control theorists, systems theorists and numerical analysts. It can also be used as a graduate course in linear time-varying system theory.

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Editorial Reviews

Provides a detailed and consistent exposition of a unifying framework for the study of time-variant systems and examines computational aspects and problems that arise in this context. This framework bridges the gap between complex analysis and linear algebra, and allows the extension of classical results from complex function theory to the case of time-variant operators and finite-dimensional matrices. These results allow the user to obtain computationally feasible schemes and models for complex and large-scale systems. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9781441950451
  • Publisher: Springer US
  • Publication date: 12/3/2010
  • Edition description: Softcover reprint of hardcover 1st ed. 1998
  • Edition number: 1
  • Pages: 460
  • Product dimensions: 0.96 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Preface. 1. Introduction. Part I: Realization. 2. Notation and Properties of Non-Uniform Spaces. 3. Time-Varying State Space Realizations. 4. Diagonal Algebra. 5. Operator Realization Theory. 6. Isometric and Inner Operators. 7. Inner-Outer Factorization and Operator Inversion. Part II: Interpolation and Approximation. 8. J-Unitary Operators. 9. Algebraic Interpolation. 10. Hankel-Norm Model Reduction. 11. Low-Rank Matrix Approximation and Subspace Tracking. Part III: Factorization. 12. Orthogonal Embedding. 13. Spectral Factorization. 14. Lossless Cascade Factorizations. 15. Conclusions. Appendices: A. Hilbert Space Definitions and Properties. References. Glossary of Notation. Index.

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