Lagrange interpolation formula
Hello readers, in today’s topic, we will discuss the Lagrange interpolation formula in numerical analysis/techniques, By using this we find the largest polynomial of a equation. Before these, we also discussed Secant Method in Numerical Analysis Regula Falsi Method In Numerical Method, if you don’t know Hurry up Now! Previously we also described briefly various topics such as BiSection Method In Numerical Techniques, Newton’s Raphson Method, and many more which are really helpful for your better understanding. So without wasting time let’s dive into our topic:
Lagrange’s interpolation is an nth degree polynomial approximation to f(x).
So the nth formula is given below
Evaluate f(0.3) by using the Lagrange interpolation formula from the following table
| x | 0 | 1 | 3 | 4 | 7 |
| f | 1 | 3 | 49 | 129 | 813 |
This question will solve by the Lagrange interpolation formula so for easy calculation first, we write the values of x and f individually.
X0= 0 , X1 =1 , x2=3 , x3=4 , x4=7
F(x0)=1 , F(x1)=3 , F(x2)=49 , F(x3)=129 ,F(x4)=813
So let’s write the Lagrange interpolation formula according to our formula
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