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Interpolation - Dictionary Definition and Overview |
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Interpolation : (noun)
1: 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" [syn: 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 [syn: interjection, interposition,
interpellation]
Based on WordNet 2.0
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Interpolation : \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.
Based on Webster's Revised Unabridged Dictionary
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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.
(1997-07-14)
Based on Webster's Revised Unabridged Dictionary (1913)
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