langrange interpolation formula

What is Interpolation

Interpolation is the process of finding a missing value in a given set of values.
Or
Interpolation is the process or Technique of finding the value of a function for any intermediate value of the independent variable.

Take an example
x0 x1 x2 x3
Now if we have to find the X1.5 value and its effect on the other equations.

Lagrange’s Interpolation


In Lagrange’s Interpolation, we only know the values of variables and there is no function given for it.
It works for both spaced and unequal spaced values of variables or data points.

Lagrange’s Interpolation is preferred over Newton’s Interpolation because it works for both equal and unequal spaced values of given data.

Formula

Lagrange’s Interpolation Formula

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langrange interpolation formula
Lagrange Formula

Solved Example

Lagrange’s Interpolation Solved Example

Q. From the following set of data points evaluate f(9) using Lagrange Interpolation?

x57111317
y=f(x)150392145223665202
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Now apply the lagrange formula to this table and solve.

Here, X = 9 that is Given f(9).

X = 9X0 = 5
X1 = 7X2 =11
X3 = 13X4 = 17

Also, value of function f( xi ).

f(x0) =150f(x1)=392
f(x2) =1452f(x3) =2366
f(x2) =5202
Lagrange interpolation example solved

Now, Simplify the polynomial

Lagrange interpolation example solved

F(9) = -16.67 + 209.07 + 1290.67 – 788.66 + 115.6
F(9) = 810 Ans.

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