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
12 - LU (Spectral) Factorization
from Part II - Further Contributions to Matrix Theory
Published online by Cambridge University Press: 24 October 2024
- 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 following five chapters exhibit further contributions of the theory of time-variant and quasi-separable systems to matrix algebra. This chapter treats LU factorization, or, equivalently, spectral factorization, which is another, often occurring type of factorization of a quasi-separable system. This type of factorization does not necessarily exist and, when it exists, could traditionally not be computed in a stable numerical way (Gaussian elimination). Here we present necessary and sufficient existence conditions and a stable numerical algorithm to compute the factorization using orthogonal transformations applied to the quasi-separable representation.
- Type
- Chapter
- Information
- Time-Variant and Quasi-separable SystemsMatrix Theory, Recursions and Computations, pp. 185 - 201Publisher: Cambridge University PressPrint publication year: 2024