|n.||1.||The act of introducing or inserting anything, especially that which is spurious or foreign.|
|2.||That which is introduced or inserted, especially something foreign or spurious.|
|3.||(Math.) The method or operation of finding from a few given terms of a series, as of numbers or observations, other intermediate terms in conformity with the law of the series.|
|Noun||1.||interpolation - a message (spoken or written) that is introduced or inserted; "with the help of his friend's interpolations his story was eventually told"; "with many insertions in the margins"|
|2.||interpolation - (mathematics) calculation of the value of a function between the values already known|
|3.||interpolation - the action of interjecting or interposing an action or remark that interrupts|
|(mathematics, algorithm)||interpolation - A mathematical procedure which
estimates values of a function at positions between listed
or given values. Interpolation 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.