Gourt > Science > Math > Numerical Analysis > Approximation Theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterising the errors introduced thereby. Note that what is meant by best and simpler will depend on the application.
One problem of particular interest is that of approximating a function in a computer mathematical library, using operations that can be performed on the computer or calculator (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or rational (ratio of polynomials) approximations.
The objective is to make the approximation as close as possible to the actual function, typically with an accuracy close to that of the underlying computer's floating point arithmetic. This is accomplished by using a polynomial of high degree, and/or narrowing the domain over which the polynomial has to approximate the function. Narrowing the domain can often be done though the use of various addition or scaling formulas for the function being approximated. Modern mathematical libraries often reduce the domain into many tiny segments and use a low-degree polynomial for each segment.
More on [ Approximation theory ]
Differential Equations with Maple, 3rd Edition
Brian R. Hunt, Ronald L. Lipsman, John E. Osborn, Jonathan M. Rosenberg Mon, 29 Sep 2008 04:00:00 -0000
Read More...
Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches
Richard Jensen, Qiang Shen Mon, 29 Sep 2008 04:00:00 -0000
Computational Intelligence and Feature Selection provides a high level audience with both the background and fundamental ideas behind feature selection with an emphasis on those techniques based on rough and fuzzy sets, including their hybridizations. It introduces set theory, fuzzy set theory, rough set theory, and fuzzy-rough set theory, and illustrates the power and efficacy of the feature selection described through the use of real-world applications Read More...
Statistical Methods in e-Commerce Research
Wolfgang Jank, Galit Shmueli Mon, 29 Sep 2008 04:00:00 -0000
This groundbreaking book introduces the application of statistical methodologies to e-Commerce data With the expanding presence of technology in today's economic market, the use of the Internet for buying, selling, and investing is growing more popular and public in nature. Statistical Methods in e-Commerce Research is the first book of its kind to focus on the statistical models and methods that are essential in order to analyze information from Read More...
Fundamentals of Quality Control and Improvement, Student Solutions Manual, 3rd Edition
Amit Mitra Mon, 22 Sep 2008 04:00:00 -0000
Incorporating modern ideas, methods, and philosophies of quality management, Fundamentals of Quality Control and Improvement, Third Edition presents a quantitative approach to management-oriented techniques and enforces the integration of statistical concepts into quality assurance methods. Utilizing a sound theoretical foundation and illustrating procedural techniques through real-world examples, Read More...
Handbook of Mathematical Relations in Particulate Materials Processing
Randall M. German Tue, 16 Sep 2008 04:00:00 -0000
Handbook of Mathematical Relations in Particulate Materials Processing goes beyond the traditional barriers of only one material class by covering the major areas in ceramics, cemented carbides, powder metallurgy, and particulate materials. Suited for quick reference with stand alone definitions. It is the perfect complement to existing textbooks since it will simply cut to the key relations. Read More...
Multivariate Methods in Chromatography: A Practical Guide
Tibor Cserhati Tue, 09 Sep 2008 04:00:00 -0000
A comprehensive, compilation and evaluation of the newest results in the field of enumerate evaluation of chromatographic data Aimed at the practicing professional, researchers and advanced students working in this area Special emphasis on practical applications While the principles of chromatography and multivariate mathematical-statistical methods are discussed separately, the book focuses on their interconnection. Read More...
A Short Course on Approximation Theory - Lecture notes for a graduate course by Neal Carothers, Bowling Green State University. (DVI,PS)
A View from the Back of the Envelope - About approximation and the fun it enables. Includes examples, exercises, and links to help grasp concepts such as measurement, scale and magnitude. Sections include simplifying numbers, exponential notation, Fermi problems, using your body as a ruler, and other ways to visualize size and scale.
Approximation and Imaging - Université de Pau. Research topics, faculty, publications, meetings.
Meta Description: [ The Harvard University Homepage: an overview
of academic programs, campus life, resources, news and events, with extensive
links to other web sites located throughout the University. ]
Approximation People - A list of home pages kept at the University of Erlangen.
Approximation Theory - Lecture notes for Part III of the Mathematical Tripos by A. Shadrin, DAMTP, University of Cambridge. (PS)
Approximation Theory - Notes for courses given by Carl de Boor, Madison. (PS)
Approximation Theory Network (AT-NET) - Publishes a Bulletin and lists journals, theses, people, events and other links.
404
Association Française d'Approximation - The subgroup of SMAI concerned with approximation and representation of curves and surfaces. Features conferences, workshops and bibliography.
404
Bibliography in the Approximation of Curves and Surfaces - Mainly in English, some French.
History of Approximation Theory - Articles and web resources developed by Allan Pinkus and Carl de Boor.
NZ Approximation Theory Group - Members, meetings, visitors and links.
404
Open Problems in Constructive Approximation - Articles in PostScript format.
People in Approximation Theory - Amos Ron's list of links.
| The substance of bourgeois theory, supply and demand, is important for understanding some things about the economy: price fluctuations, inf | |
| Next Video | |
