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On Condition Numbers and the Distance to the Nearest Ill-Posed Problem (Classic Reprint) - Softcover
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Excerpt from On Condition Numbers and the Distance to the Nearest Ill-Posed Problem
The condition number of a problem measures the sensitivity of the answer to small changes in the input. We call the problem ill-posed if its condition number is infinite. The ill-posed problems typically form a lower dimensional surface in the space of problems. It turns out that for many problems of numerical analysis, there is a simple relationship between the condition number of a problem and the shortest distance from that problem to the surface of ill-posed ones: the shortest distance is proportional to the reciprocal of the condition number, or bounded by the reciprocal of the condition number. Sometimes, the distance is bounded below by the reciprocal of the condition number squared. This is true for matrix inversion, computing eigenvalues and eigenvectors, finding zeros of polynomials.
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- VerlagForgotten Books
- Erscheinungsdatum2018
- ISBN 10 1334018197
- ISBN 13 9781334018190
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten66
- Kontakt zum HerstellerNicht verfügbar
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On Condition Numbers and the Distance to the Nearest IllPosed Problem Classic Reprint
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781334018190
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On Condition Numbers and the Distance to the Nearest IllPosed Problem Classic Reprint
Anbieter: PBShop.store UK, Fairford, GLOS, Vereinigtes Königreich
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781334018190
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On Condition Numbers and the Distance to the Nearest Ill-Posed Problem
Print-on-DemandAnbieter: Forgotten Books, London, Vereinigtes Königreich
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Paperback. Zustand: New. Print on Demand. This book explores the relationship between the condition number of a problem, a measure of how much its solution changes in response to small changes in its data, and the distance to the nearest ill-posed problem, a problem with an infinite condition number. The author shows that for many important problems, including matrix inversion, eigenvalue computation, and polynomial root finding, the condition number can be used to estimate how close a problem is to being ill-posed. This estimate can be used to determine how much effort should be put into solving a problem, and to guide the development of algorithms for solving ill-posed problems. 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 9781334018190_0
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