Approximation


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Related to Approximation: joint approximation, Approximation algorithms

approximation

[ə¦präk·sə¦mā·shən]
(mathematics)
A result that is not exact but is near enough to the correct result for some specified purpose.
A procedure for obtaining such a result.

Approximation

 

replacement of certain mathematical objects by others which are in one sense or another close to the initial objects. Approximation makes it possible to study the numerical characteristics and qualitative properties of the object, reducing the problem to a study of simpler or more convenient objects—for example, objects whose characteristics are easily computed or whose properties are already known. The theory of numbers studies Diophantine approximations—in particular, approximations of irrational numbers by rational numbers. Approximations of curves, surfaces, spaces, and mappings are investigated in geometry and topology. Some branches of mathematics are wholly devoted to approximations, as, for example, the approximation and interpolation of functions and numerical methods of analysis. The role of approximation in mathematics is continually growing. Presently, approximation can be viewed as one of the basic concepts of mathematics.

S. B. STECHKIN

References in periodicals archive ?
Clearly the approximation is too crude to illustrate the appearance of the (m,1#) mode.
The first purpose of this article is to see approximation of the operators (4) in the space of continuous functions.
According to this fact, we look in Section 4 for an approximation in the same Krylov subspace which actually minimises the energy backward error.
Berinde: On the approximation of fixed points of weak contractive mappings, Carpathian J.
For the method of successive approximation [4, 6] the equation (1) can be written as
Key words: eigenvalue problem, Toeplitz matrix, (2,3)-Pade approximation
The aim of this contribution is the description of error estimates for the approximation of operators by multiple and generalized Gabor multipliers.
In order to generate a mathematical approximation, the analyzed data must be properly prepared.
International Workshop on Orthogonal Polynomials and Approximation Theory (2008: Madrid, Spain) Ed.
Thus, T can be viewed as a closed set of real numbers superimposed over the interval [a, b] from an approximation point-of-view.
In the known solutions for progressive transmission, the generalization of the vector data is performed by multiresolution polygonal approximation with the heuristic split-based (Zhou and Bertolotto, 2004a, 2004c) or merge-based algorithms (Yang, 2005; Yang et al.
Some authors acknowledge that larger n may be needed for some population distributions (Aczel and Sounderpandian (2006)), but even with such disclaimers, these authors give no indication of how much larger n may need to be in order that approximation using the CLT is satisfactory.