extrapolate

extrapolate
    v 1: draw from specific cases for more general cases [syn:
         {generalize}, {generalise}, {extrapolate}, {infer}]
    2: estimate the value of [syn: {interpolate}, {extrapolate}]
    3: gain knowledge of (an area not known or experienced) by
       extrapolating
    

extrapolation
extrapolate
interpolation

   <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.

   (2007-06-29)