Computing Stable Elgendecompositions of Matrix Pencils (Classic Reprint)
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.35
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Add to basketItem description from seller
Print on Demand. This book offers insights into the mathematical theory behind the study of a specific kind of matrix called a matrix pencil. Matrix pencils arise in many applications, such as engineering, physics, and economics, and their analysis is crucial for understanding the behavior of complex systems. The author provides a detailed exploration of the theory of matrix pencils, delving into their stability and properties. Notably, the book presents novel criteria for determining the stability of matrix pencils, enabling researchers to assess the accuracy and reliability of their results. These criteria are crucial for designing efficient and robust algorithms for solving problems involving matrix pencils. Moreover, the book explores the application of matrix pencil theory to the analysis of control systems, providing valuable insights into the behavior and controllability of complex dynamical systems. Through its rigorous analysis and practical applications, this book offers a comprehensive understanding of matrix pencil theory, making it an indispensable resource for researchers and practitioners in various fields. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781332899012_0
- Title
- Computing Stable Elgendecompositions of Matrix Pencils (Classic Reprint)
- Author
- James Weldon Demmel, Bo Kågstrà m
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1332899013
- ISBN 13
- 9781332899012
- Seller catalogs
- Geometry
In clear terms, the work introduces criteria to decide if a decomposition is stable, discusses the Kronecker Canonical Form, and shows how to bound how much the defining matrices P, Q, S, and T can change as A and B vary. It also connects theory to practical questions in controllability and observability, and describes how to verify stability using computable quantities.
- Shows how perturbations influence the spectrum and deflating subspaces of A − λB.
- Defines measurable bounds that determine when a decomposition remains valid across pencils in a family P(ε).
- Relates stability to condition numbers of the deflating subspaces and to the sizes of finite and infinite eigenvalue blocks.
- Applies to control system concepts like controllability and observability subspaces with a perturbation perspective.
Ideal for readers of advanced linear algebra and numerical analysis who want a rigorous treatment of stability in generalized eigenproblems and practical criteria for deciding when a decomposition is reliable.
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Forgotten Books
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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