Approximation


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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 ?
As we know from the trigonometric Fourier approximation, the strong convergence of the Fourier partial sums is not guaranteed for all f [member of] X.
Saddlepoint approximation has been used in [8] for multi-disciplinary RBDO.
truncat] denote the error caused by approximation algorithm and truncation, respectively.
A rough standard neutrosophic set is the approximation of a standard neutrosophic set w.
It can be seen in Figure 1 that at the edges of the interval the approximation error is larger than in the middle of the interval.
In this section, we introduce rough type-2 fuzzy approximation operators and generalized rough type-2 fuzzy approximation operators induced from the Pawlak approximation space and the generalized Pawlak approximation space, respectively, and discuss their properties.
However brought to [1,2] mathematical solution of a problem of approximation it is applicable only to one-dimensional dependences.
p] approximation theorem for the sequence of positive linear operators.
The literature review shows that one of the most common mathematical tools to deal with periodical functions is the Fourier expansion, which is an approximation used to rebuild curves based on sinusoidal signals.
In the next approximation the flat plate is replaced by a curved section of the bell, and again the inadequacy of the model is evidenced in figures 8.
The first purpose of this article is to see approximation of the operators (4) in the space of continuous functions.
Recently a novel approximation scheme, the generalized meshfree (GMF) approximation method [16], was developed to enhance the smoothness of the approximation as well as to generate the desired weak Kronecker-delta property [16] at the boundary.