Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Part I Lectures on Basics with Examples
- Part II Further Contributions to Matrix Theory
- 12 LU (Spectral) Factorization
- 13 Matrix Schur Interpolation
- 14 The Scattering Picture
- 15 Constrained Interpolation
- 16 Constrained Model Reduction
- 17 Isometric Embedding for Causal Contractions
- Appendix: Data Model and Implementations
- References
- Index
15 - Constrained Interpolation
from Part II - Further Contributions to Matrix Theory
Published online by Cambridge University Press: 24 October 2024
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Part I Lectures on Basics with Examples
- Part II Further Contributions to Matrix Theory
- 12 LU (Spectral) Factorization
- 13 Matrix Schur Interpolation
- 14 The Scattering Picture
- 15 Constrained Interpolation
- 16 Constrained Model Reduction
- 17 Isometric Embedding for Causal Contractions
- Appendix: Data Model and Implementations
- References
- Index
Summary
The chapter shows how classical interpolation problems of various types (Schur, Nevanlinna–Pick, Hermite–Fejer) carry over and generalize to the time-variant and/or matrix situation. We show that they all reduce to a single generalized constrained interpolation problem, elegantly solved by time-variant scattering theory. An essential ingredient is the definition of the notion of valuation for time-variant systems, thereby generalizing the notion of valuation in the complex plane provided by the classical z-transform.
- Type
- Chapter
- Information
- Time-Variant and Quasi-separable SystemsMatrix Theory, Recursions and Computations, pp. 242 - 253Publisher: Cambridge University PressPrint publication year: 2024