Using the inverse Lagrange’s interpolation, find the value of x

Question

Using the inverse Lagrange’s interpolation, find the value of x when y=3 for the following data:
x 25 35 55 75
y=f(x) -2 -1 1 5

02 Aug 2023

Answer :

Word Count : 451

To find the value of x when y = 3 using inverse Lagrange's interpolation, we need to reverse the roles of x and y in the interpolation process. Instead of interpolating y values for given x values, we will interpolate x values for a given y value.

Given data:
x: 25 35 55 75
y: -2 -1 1 5

Inverse Lagrange's interpolation involves the following steps:

Step 1: Calculate the Lagrange basis polynomials for each data point. The Lagrange basis polynomials are given by:

L_i(x) = Π [(x - x_j) / (x_i - x_j)], where i ≠ j

For our data, we have:
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