Inhaltsangabe
Understand how small changes affect generalized eigenstructures in matrix pencils. This book explains a framework for computing stable decompositions of pencils A − λB, focusing on when the decomposition remains valid as the data varies within a tolerance. It links perturbation bounds to the block structure that reveals regular and singular parts, including left and right deflating subspaces.
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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Computing Stable Elgendecompositions of Matrix Pencils (Classic Reprint)
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Paperback. Zustand: New. 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. print-on-demand item. Bestandsnummer des Verkäufers 9781332899012_0
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Computing Stable Elgendecompositions of Matrix Pencils Classic Reprint
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