Complexity and Information
Complexity and Information
A. G. Werschulz, Fordham University and Columbia University, New York
$59.99
USDThe 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.
- First book for a general audience on the computational complexity of continuous models of science
- Coverage of new, improved methods for mathematical finance
- Comprehensive bibliography covering the last decade's progress in this exciting area
Reviews & endorsements
"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
Product details
January 1999Paperback
9780521485067
154 pages
216 × 140 × 9 mm
0.2kg
10 b/w illus. 5 tables
Available
Table of Contents
- Part I. Fundamentals:
- 1. Introduction
- 2. Information-based complexity
- 3. Breaking the curse of dimensionality
- Part II. Some Interesting Topics:
- 4. Very high-dimensional integration and mathematical finance
- 5. Complexity of path integration
- 6. Are ill-posed problems solvable?
- 7. Complexity of nonlinear problems
- 8. What model of computation should be used by scientists?
- 9. Do impossibility theorems from formal models limit scientific knowledge? 10. Complexity of linear programming
- 11. Complexity of verification
- 12. Complexity of implementation testing
- 13. Noisy information
- 14. Value of information in computation
- 15. Assigning values to mathematical hypotheses
- 16. Open problems
- 17. A brief history of information-based complexity
- Part III. References:
- 18. A guide to the literature
- Bibliography
- Subject index
- Author index.
