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 ?
We introduce the accelerating parameter [alpha] to Successive Approximation Method (3).
In each step of the successive approximation method, a Fredholme integral of order II is obtained, for which, using the supraposition rule of flow potentials, we seek solutions of the form:
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.
5) hold and consider the successive approximation Method
The COP8CBR's integrated 10-bit successive approximation analog-to-digital converter (ADC) provides the analog multiplexer's output signal to an output pin and an A/D direct input.
These products include Analog Devices' ADM6319, a supervisory circuit that monitors power supply voltage levels and code execution integrity in microprocessor-based systems; the AD7478 8-bit, low-power, (SAR) successive approximation analog-to-digital converter (ADC); the AD9280 single-supply, 8-bit, 32 MSPS ADC; and the ADuC7032 precision battery monitor sensor, a complete system solution for battery monitoring in 12V automotive applications.
New successive approximation register architecture for 12-bit ADCs supports conversion rates up to 320 MSPS
It is micro power, 2-channel, 12-bit successive approximation sampling A/D converter which can operate on 5V to 9V power supplies.
His ideas and work have blurred the distinctions between sigma delta, successive approximation and pipelined converter architectures, and have resulted in performance improvements in a range of ADI products, including the AD7982 and the AD7767 SAR analog-to-digital converters.

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