WordNet Dictionary- [n] the action of interjecting or interposing an action or remark that interrupts
- [n] (mathematics) calculation of the value of a function between the values already known
- [n] 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"
Webster's 1913 Dictionary\In*ter`po*la"tion\, n. [L. interpolatio an
alteration made here and there: cf. F. interpolation.]
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.
Bentley wrote a letter . . . . upon the scriptural
glosses in our present copies of Hesychius, which he
considered interpolations from a later hand. --De
Quincey.
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.
Computing DictionaryA 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.
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