Lagrange’s interpolation formula
The Newton’s forward and backward interpolation formulae can be
used only when the values of x are at equidistant. If the values of x
are at equidistant or not at equidistant, we use Lagrange’s interpolation
formula.
Let y = f( x) be a function such that f ( x) takes the values y0
, y1 , y2 ,......., yn corresponding to x= x0
, x1, x2 ..., xn That is yi = f(xi),i
= 0,1,2,...,n . Now, there are (n + 1) paired values (xi, yi),i = 0, 1, 2, ..., n and hence
f ( x) can be represented by a polynomial function of degree n in x.
Then the Lagrange’s formula is
Example 5.22
Using Lagrange’s interpolation formula find y(10) from the
following table:
Solution:
Here the intervals are unequal. By Lagrange’s interpolation
formula we have
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