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 ?
Accelerating convergence of successive approximation method will always converge if the equation (3) converges.
Using numerical integration methods in conjunction with the successive approximation method, from (10) we get [[psi].
It is well known that in Ito's classical theory of stochastic differential equations with Lipschitz continuous coefficients, the solutions are constructed on a given Brownian motion through Picard [5] successive approximation and the uniqueness of solutions is shown immediately by the construction.
Although the details of applying successive approximation apply primarily to an ideal situation and are somewhat labored, I can see the usefulness to someone wanting to apply the concepts immediately.
With the characteristics of successive approximation, the higher resolution the images implies a higher resolution watermark will be extracted.
Thus Giere seeks an account of science that will bring naturalism back from Laudan's agnosticism about successive approximation to the truth: `There is room for a modest yet robust scientific realism that insists scientists are at least sometimes successful in their attempts to represent the causal structure of the world' (p.
Their four-phase experimental structure provides the four-part structure of the novel, but the pervasive mathematical allusions point to successive approximation as the tool for expressing other aspects of the self When Watt prepares his series of dogs to eat the remnants of Mr.
The reader will be introduced to such new terms as successive approximation A/D converters and series feed-forward A/D converters.
Successive approximation is the main approach used to obtain "close-enough" solutions to equations that have no closed-form solutions.
Because these MCUs are low power consuming, the series has traditional successive approximation ADC as well RC-type ADC, which are optimized for accurate and low cost temperature and humidity monitoring, and can drive a wide array of LCD panels.
4 mW/m2, while fast readings in under 5 ms are possible using successive approximation techniques, as demonstrated in Vishays Fast Proximity Sensor software.
Part II, "Learning About the Consequences of One's Behavior," covers operant conditioning and related ideas, including reinforcers as sources of incentive motivation, successive approximation, differential and partial reinforcement, making choices, inference and the similarities between operant conditioning and natural selection.

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