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# Lagrange‚Äôs interpolation formula

The Newton‚Äôs forward and backward interpolation formulae can be used only when the values of x are at equidistant.

Lagrange‚Äôs interpolation formula

The Newton‚Äôs 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‚Äôs 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‚Äôs formula is Example 5.22

Using Lagrange‚Äôs interpolation formula find y(10) from the following table: Solution:

Here the intervals are unequal. By Lagrange‚Äôs interpolation formula we have Tags : Example Solved Problems with Answer, Solution, Formula , 12th Business Maths and Statistics : Chapter 5 : Numerical Methods
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12th Business Maths and Statistics : Chapter 5 : Numerical Methods : Lagrange‚Äôs interpolation formula | Example Solved Problems with Answer, Solution, Formula