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 ?
Moreover, Nashed and Votruba (see [1]) raised the following study suggestion: "the problem of obtaining selections with nice properties for the metric generalized inverse merits is worth studying." In [2] upper semicontinuity of the setvalued metric generalized inverse [T.sup.[partial derivative]] in approximatively compact Banach spaces is investigated by means of the methods of geometry of Banach spaces.
Our results show that the effective mass corresponding to the effective temperature is approximatively the average one in any dimension.
In fact, OSMLD codes are a subclass of LDPC codes currently present in most telecoms standards, but can be decoded iteratively by ITDA which is less complex than belief propagation algorithm with approximatively the same performances.
Ketterer (2014) also examined wind power in German electricity markets and found that an additional RES generation by 1GWh led to a reduction of daily spot price by approximatively 1[euro]/MWh.
The computational time needed to complete the whole loop is approximatively two to three hours with four CPUs depending of the loading speed during the CAI simulation (the Perl script runs without a few seconds).
On average, we see the mobile broadband traffic approximatively doubling every year globally, with the same trend also seen in MEA.
(11) Retrorenal colon is found in approximatively 0.6% of the general population according to the Hadar-Gadot and Sherman et al.
- Manufacturing and delivery of approximatively 1,550 kilometres of fibre optic cable which will facilitate bi-directional communication feed from the pipeline and associated assets, such as compressor stations and block valve stations, to the supervisory control center.
Therefore, many physical laws function approximatively (see [5]).
That means that we have approximatively 4.379.379.685 people for whom terms like digital democracy or digital activism do not mean anything.