Hello readers, in today’s topic, we will discuss the Lagrange Interpolation Formula in numerical analysis/techniques, its formula, derivation, advantages, and limitations with examples. This is a very important method to find out the largest polynomial. Before these, we also discussed about Regula Falsi Method In Numerical Method, and Secant Method in Numerical Analysis/Techniques if you don’t know Hurry up Now! Previously we also describe 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 Interpolation Formula in Numerical Analysis/Techniques
Basically in this post, we are discourse about the Lagrange interpolation and its formula. By using this formula we find the largest polynomial.
Lagrange interpolating polynomials give no error calculation.
Lagrange’s interpolation is an nth-degree polynomial approximation to f(x). So the nth formula is given below:
What is meant by a Lagrange polynomial?
In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of the lowest degree that interpolates a given set of data.
Are Newton and Lagrange the same?
The main difference between Newton and Lagrange interpolating polynomials lies only in the computational aspect. The advantage of Newton’s interpolation is the use of nested multiplication and the relative easiness to add more data points for higher-order interpolating polynomials.
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 |
Solution:
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
Then we put the above formula, we get:
So the f(0.3) by using the Lagrange interpolation formula the polynomial is 1.831.
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