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

Sinopsis

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.

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