Description: Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It shows that quantitative approximation methods penetrate and are applied in many diverse and important mathematical research fields. These areas of application include neural networks, wavelets, partial differential equations, semigroups of operators, probability and statistics, functional analysis, approximation theory, and classical analysis. The author describes all of the pertinent mathematical entities precisely and concretely, and includes all major research results from the past 15 years.
Review Quotes: "George Anastassiou has done a tremendous job in showing the diversity of quantitative approximation methods...I am pleased to see an enormous collection of essential quantitative results...there is no doubt that this book should be on the desk of any student or specialist with interests in approximation, limit theorems, and more broadly quantitative mathematical methods and their applications" -Zari Rachev, University of California, Santa Barbara "The emphasis of the results presented in this monograph is quantitative, thus, for example, all mathematical entities such as operators or constants are defined precisely. This makes the material accessible to a wide audience of graduate students and scientists. The book is well written and contains a very extensive summary of the author's work over the last fifteen years." --Steven B. Damelin, in Mathematical Reviews, Issue 2001h