Measures and differential equations in infinite-dimensional space : Yu.L. Dalecky and S.V. Fomin, Kluwer, Dordrecht, 1991. 337 pp., Dfl.220, US$126, UK£75, ISBN 0-7923-1517-0

✍ Scribed by W.F. Ames; C. Brezinski

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 146 KB
• Volume: 34
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/0378-4754(92)90061-k

✦ Synopsis

This is a study of the computational complexity of real functions in the model of discrete complexity theory. Traditionally, numerical analysis provides only upper bounds for numerical problems. The main feature of this book is to apply the newly developed NP-completeness theory to prove lower bounds for basic numerical operations, such as maximization and integration. In fact, the inherent computational complexity of basic numerical operations forms a hierarchy that is parallel to the complexity hierarchy in discrete complexity theory. These results provide a direct link between discrete complexity theory and complexity theory of continuous functions. The book includes a review of the fundamental notions in complexity theory and detailed discussions of various computational models for real continuous functions.