# interpolation meaning

Noun: interpolation  in`turpu'leyshun
1. A message (spoken or written) that is introduced or inserted
"with the help of his friend's interpolations his story was eventually told"
- insertion
2. (mathematics) calculation of the value of a function between the values already known
3. The action of interjecting or interposing an action or remark that interrupts
- interjection, interposition, interpellation

Derived forms: interpolations

Encyclopedia: Interpolation

[Economics]
Inserting missing data into a series. This is normally done by assuming that the data grew according to some known rule over the period when data are missing. Except in the case of series which are known to grow in a smooth manner, this procedure is extremely unreliable.

[Electronics]
Finding a value that falls between two values listed in a table, indicated by a dial, plotted on a graph, derived by estimate, or given by intermediate calculation. For example, if a linear variable capacitor has a value of 100 pF when its dial is set to 10, and 140 pF when the dial is set to 20, then the capacitance when the dial reads 15 (midway between 10 and 20) can be assumed to be 120 pF (midway between 100 pF and 140 pF). When functions are not linear, interpolation is usually not exact.

interpolation
interpolation meter See INTERPOLATION-TYPE INSTRUMENT.

[Finance]
A method of approximating a price or yield that is unknown by using numbers that are known.

[Computer]
<mathematics, algorithm> A mathematical procedure which estimates values of a function for certain desired inputs given values for known inputs.

If the desired input is outside the range of the known values this is called extrapolation, if it is inside then it is called interpolation.

The method works by fitting a "curve" (i.e. a function) to two or more given points and then applying this function to the required input. Example uses are calculating trigonometric functions from tables and audio waveform sythesis.

The simplest form of interpolation is where a function, f(x), is estimated by drawing a straight line ("linear interpolation") between the nearest given points on either side of the required input value:

` f(x) ~ f(x1) + (f(x2) - f(x1))(x-x1)/(x2 - x1) `
There are many variations using more than two points or higher degree polynomial functions. The technique can also be extended to functions of more than one input.

## Examples

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1. the isoclinics listed with irregular parameters can be found by interpolation.
2. interpolation between satellite positions was initially carried out by dead-reckoning procedures.
3. for intermediate doses, the corresponding slant distances can be estimated by interpolation.
4. statistical error-correction and interpolation routines will generally produce track plots to an absolute accuracy of 100 to 200 ft.
5. the directions can be obtained by removing the quarter-wave plate and following the procedure for plane polarized light or by interpolation.