The Probability That a Numerical, Analysis Problem Is Difficult

James W. Demmel

ISBN 10: 1330257162 / ISBN 13: 9781330257166

Published by Forgotten Books, 2018

About this Item

Print on Demand. This book explores the likelihood that a numerical analysis problem will be difficult, the circumstances surrounding the circumstances that raise the difficulty, and statistical methods for understanding the frequency of these difficulties. Through this analysis, the author positions these problems within their broader historical context and presents a methodology to increase the probability that a problem will have a solution, which extends the applicability of numerical methods to new classes of 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.

Seller Inventory # 9781330257166_0

Bibliographic Details

• Title: The Probability That a Numerical, Analysis Problem Is Difficult
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 1330257162
• ISBN 13: 9781330257166
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Statistics

About this title

Synopsis

Discover how likely numerical problems are to be hard—and why some problems stay solvable.

This book explains a probabilistic way to study numerical conditioning, showing how the distance to ill-posed problems affects accuracy and behavior in algorithms. It ties geometry, probability, and computer arithmetic into a practical view of when and why numerical methods work.

• Learn the idea that a problem’s condition number connects to how close it is to infinite sensitivity, and how this guides algorithmic reliability.
• See how uniform distributions and tubular neighborhoods help bound the chances of large errors in matrix inversion, polynomial zero finding, and eigenvalue computations.
• Understand how finite precision arithmetic changes the picture, and what this means for real-world computations and algorithm design.
• Explore the limits of the probabilistic model, including when discretization or clustering near ill-posed sets alters expected outcomes.

Ideal for readers who want a clear, theory-grounded view of numerical analysis, conditioning, and the practical behavior of algorithms in computing.