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in⋅ter⋅po⋅la⋅tion

[in-tur-puh-ley-shuh

–noun

1.	the act or process of interpolating or the state of being interpolated.

2.	something interpolated, as a passage introduced into a text.

Mathematics.

a.	the process of determining the value of a function between two points at which it has prescribed values.

b.	a similar process using more than two points at which the function has prescribed values.

c.	the process of approximating a given function by using its values at a discrete set of points.

Origin:
1605–15; < L interpolātiōn- (s. of interpolātiō). See interpolate, -ion

Dictionary.com Unabridged (v 1.1)
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006.
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in·ter·po·late   (ĭn-tûr'pə-lāt') Pronunciation Key
v.   in·ter·po·lat·ed, in·ter·po·lat·ing, in·ter·po·lates

v.   tr.

To insert or introduce between other elements or parts.
1. To insert (material) into a text.
2. To insert into a conversation. See Synonyms at introduce.
To change or falsify (a text) by introducing new or incorrect material.
Mathematics To estimate a value of (a function or series) between two known values.

v. intr.
To make insertions or additions.

[Latin interpolāre, interpolāt-, to touch up, refurbish, from interpolis, refurbished; see pel-⁵ in Indo-European roots.]

in·ter'po·la'tion n., in·ter'po·la'tive adj., in·ter'po·la'tor n.

The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2006 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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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"
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]

WordNet® 3.0, © 2006 by Princeton University.
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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)

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.

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