interpolation

mathematics, algorithm 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.

(1997-07-14)