On Condition Numbers and the Distance to the Nearest Ill-Posed Problem (Classic Reprint): December 1985 - Couverture souple

Demmel, James

9781332890002: On Condition Numbers and the Distance to the Nearest Ill-Posed Problem (Classic Reprint): December 1985

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ISBN 10 : 1332890008 ISBN 13 : 9781332890002

Editeur : Forgotten Books, 2018

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Explore how small changes near ill-posed problems reveal big shifts in stability across core numerical tasks. This work shows a unifying view of condition numbers and distance to the nearest ill-posed problem, with concrete links to matrix inversion, eigenvalue computations, polynomial zeros, and pole assignment in control systems.

In clear terms, the book explains how the reciprocal of a condition number bounds how far a problem is from becoming ill-posed. It uses locally available information to answer a global question: how close is the nearest ill-posed case in several important problem classes? The discussion includes differential inequalities, explicit bounds, and practical implications for common numerical tasks, organized to let readers explore each topic independently.

- See how a problem’s sensitivity relates to its distance from ill-posedness.
- Learn the differential-inequality approach and how it yields upper and lower distance bounds.
- Compare results across matrix inversion, eigensystems, polynomial roots, and pole assignment.
- Understand the role of norms and gradients in deriving robust estimates.

Ideal for readers of advanced linear algebra and numerical analysis who want a cohesive framework for stability and conditioning in key computational problems, presented with accessible math and usable insights.

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�diteur: Forgotten Books
Date d'�dition: 2018
Langue: anglais
ISBN 10: 1332890008
ISBN 13: 9781332890002
Reliure: Broch�
Nombre de pages: 27
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On Condition Numbers and the Distance to the Nearest Ill-Posed Problem

James Demmel

Edit� par Forgotten Books, 2018

ISBN 10 : 1332890008 ISBN 13 : 9781332890002

Neuf Paperback

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Vendeur : Forgotten Books, London, Royaume-Uni

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Paperback. Etat : New. Print on Demand. This book focuses on the relationship between a problem's condition number and the distance to the nearest ill-posed problem. The condition number measures the sensitivity of the answer to small changes in the input, and an ill-posed problem is one with an infinite condition number. The author shows that for many problems in numerical analysis, there is a simple relationship between the condition number and the distance to the nearest ill-posed problem. This relationship is explained using differential inequalities and can be used to derive upper and lower bounds on the distance to the nearest ill-posed problem. The author also discusses the implications of this relationship for the conditioning of matrix inversion, eigendecompositions, polynomial zero finding, and pole assignment in linear control systems. Overall, this book provides a unified and insightful approach to understanding the conditioning of numerical problems and the distance to the nearest ill-posed problem. 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. N� de r�f. du vendeur 9781332890002_0

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