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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
As for the numerical value in (11) and (12) of the dimensionless adiabatic index [[gamma].sub.a], for the equilibrium heat-radiating system <<high-current plasma discharge channelair>> it is approximately equal to [[gamma].sub.a] [approximately equal to] 4/3 [10].
From (2) at [h.sub.sm] [approximately equal to] 2 mm, [[rho].sub.s] [approximately equal to] 72.5 x [10.sup.-8] [OHM] x m, [D.sub.se] [approximately equal to] 80 mm and [D.sub.si] [approximately equal to] 10 mm it follows that the sought value of RS0 is approximately equal to 0.12 m[OHM].
As in the UCLA study, the new and old vaccines boosted pertussis antibodies in approximately equal measures, and side effects with the new vaccine were significantly rarer than with the old one.
So, taking into account (1) for copper conductor ([n.sub.e0] = 16.86 x [10.sup.28][m.sup.-3] [10]) at [[delta].sub.0m] = 4 x [10.sup.6] A/[m.sup.2] typical for normal operation of industrial electric alternating current networks [13], we find that it [DELTA][z.sub.nh] width is approximately equal to 0.53 m.
In addition, we believe that the average concentration (bulk density) [n.sub.e0] free electrons in the case of flow along the plasma channel lightning long-term C-component of the lightning current also remained the same and approximately equal [n.sub.e0] [approximately equal to] [10.sup.25] [m.sup.-3].
Found in a copper conductor RF cable PK [??]2-3,5/9 with PET insulation for the case ([I.sub.mL] [approximately equal to] 85.6 [kappa]A; [J.sub.L] [approximately equal to] 2 x [10.sup.-6] [A.sup.2] x s) calculated by taking into account [15] The peak value of the maximum permissible density [delta]m1d current pulse 15/335 [micro]s of the artificial lightning from the ratio [[delta].sub.m1d] = 1.353 x [10.sup.8] x [I.sub.mL]/[([J.sub.L]).sup.1/2] is approximately equal to [[delta].sub.m1d] [approximately equal to] 8.2 [kappa]A/[mm.sup.2].
We also use the fact that the neutron energy E of interest is approximately equal to [E.sub.p] (k and [[kappa].sub.f] are the neutron wavenumbers corresponding to E and [S.sub.n.sup.f], respectively).
The production index for other durable consumer goods has changed little in the past two months and approximately equaled its average level in both 1994 and 1995.
Here, the averaged power P consumed in the WCH with water approximately equals P = [E.sub.wch]/T = 44.8 kJ/10 s [approximately equal to] [approximately equal to] 4.5 kW.

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