Complexity and Information (Lezioni Lincee) [Paperback]

J. F. Traub (Author), A. G. Werschulz (Author)

Book Description

ISBN-10: 0521485061 | ISBN-13: 978-0521485067 | Publication Date: January 13, 1999

The twin themes of computational complexity and information pervade this book. It starts with an introduction to information-based complexity, that is, the computational complexity of continuous mathematical models. It then moves to a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, value of information in computation, assigning values to mathematical hypotheses, and mathematical finance. The style is informal, and the goal is motivation and insight. Precise statements and proofs can be found in the monographs and papers included in the comprehensive bibliography. The book will be essential reading for researchers in the many disciplines influenced by the computational complexity of continuous problems.

Editorial Reviews

Review

"This short volume packs so much information into so small a space that it stretches the imagination as to know how the authors did it. Clearly written, filled with interesting examples, important theorems and tantalizing conjectures, this book should be taken as holiday reading by everyone concerned with using a computer to solve real problems. It's destined to be a classic." New Scientist

"The exposition is straightforward and clear, with well-chosen diagrams to smooth the way...The broad expanse between technical and general themes may be one of the more challenging and appealing aspects of the book...This book provides worthwhile evidence that IBC (information based complexity) is an important, albeit highly specialized, approach to understanding and applying information in modeling the complexity of a variety of mathematically formulated problems." Complexity

"...gives a good grounding in the essential issues of complexity and information. For an overview of the larger issues, this small book is excellent." Bulletin of the AMS

"Really a jewel...written with loving care and in an elegant style." Institute of Discrete Mathematics

"Highly recommended." Choice

"Anyone interested in numerical analysis and scientific computing can profit from the book and its many insights." Siam Review

Book Description

The twin themes of of computational complexity and information pervade this book. Information-based complexity is used to illustrate a variety of topics, including breaking the curse of dimension, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance.The style is inf ormal, and the goals are exposition, insight and motivation. As the first introductory book on the subject it will invaluable as a guide to the area.

Product Details

• Paperback: 154 pages
• Publisher: Cambridge University Press (January 13, 1999)
• Language: English
• ISBN-10: 0521485061
• ISBN-13: 978-0521485067
• Product Dimensions: 8.5 x 5.5 x 0.4 inches
• Shipping Weight: 6.7 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,904,901 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

4.0 out of 5 stars a wonderful little book, a lot packed in a few pages., May 3, 1999

By A Customer

This review is from: Complexity and Information (Lezioni Lincee) (Paperback)

I found the book a good introduction to IBC(informatin based complexity)and highly readable. The author raises a considerable number of interesting problems and questions and sketches out some interesting results. This is an excellent book for anyone interested in numerical methods around integration, complexity, computability,tractability, ill posed problems in general. An amazing number of open problems are discussed for anyone looking for research projects and these range from problems that may be doable to those that look virtually impossible. I found the use of a real-number model of computing a powerful change from Turing model. The overall strength of the book is the exposure to new ideas involving computational models, and how these ideas can help one solve and approach computational problems of both a theoretical and a practical nature -- particularly those involving "real" numbers.