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Linear interpolation

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A method for the approximate calculation of the value of a function , based on the replacement of by a linear function

the parameters and being chosen in such a way that the values of coincide with the values of at given points and :

These conditions are satisfied by the unique function

which approximates the given function on the interval with error

The calculations necessary for linear interpolation are easily realized by hand; for this reason this method is widely used for the interpolation of tabular data.

References

[1] N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from Russian)
[2] I.S. Berezin, N.P. Zhidkov, "Computing methods" , Pergamon (1973) (Translated from Russian)


Comments

References

[a1] P.J. Davis, "Interpolation and approximation" , Dover, reprint (1975) pp. 108–126
[a2] J.F. Steffensen, "Interpolation" , Chelsea, reprint (1950)
How to Cite This Entry:
Linear interpolation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_interpolation&oldid=27067
This article was adapted from an original article by M.K. Samarin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article