Skip to content
site-logo
  • Home
  • JavaScript
  • Machine Learning
  • C++Expand
    • C++ Programing
    • Numerical Techniques C++
    • Data Structures C++
    • C++ Programs
  • Typing Guide
  • Blogs
site-logo
Home / Numerical Techniques C++ / Lagrange Interpolation Formula with Solved Example

Lagrange Interpolation Formula with Solved Example

ByLonz Updated onMarch 8, 2021
Numerical Techniques C++
langrange interpolation formula
Ad
Table of contents
  1. What is Interpolation
  2. Lagrange’s Interpolation
  3. Formula
  4. Solved Example
    1. Q. From the following set of data points evaluate f(9) using Lagrange Interpolation?
  5. Related Posts

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.

Ad

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

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

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

Ad
Lagrange interpolation example solved

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

Related Posts

  • Intermediate value property
    Ad If f(x) is continuous in the interval [a,b] and f(a1) ,f(b1) have different signs,…
  • bisection method c++ program
    Bisection method C++ Program | Algorithm & Solved Example
    The bisection method is explained easy step by step with algorithm and images. Bisection method with c++ code program algorithm example
  • graphical explanation
    Regula Falsi Method with C++ Program | Example & Algorithm
    Regula Falsi Method C++ Program Example and Algorithm. Regula falsi method is also called the method of false method.
  • newton-raphson method
    Newton-Raphson Method C++ Program / Example Formula
    Algorithm and concept of newton raphson method c/c++ explained step by step for beginners as well as experienced stduents of numerical techniques using c++
  • Binary Representation of Numbers | How numbers are represented in Binary
    Binary number system is useful because all of the computers store information in binary form. i.e combination of 0s and 1s.

Post navigation

Previous Previous
Implement Stack Using Linked List C++ Program
NextContinue
Find the Regression line of y on x. Evaluate the value of y when x = 10?
Search

  • Home
  • Privacy Policy
  • Disclaimer
  • Sitemap
  • Write for us
  • Contact Us

Copyright © 2025 TechInDetail

Scroll to top
  • Home
  • JavaScript
  • Machine Learning
  • C++
    • C++ Programing
    • Numerical Techniques C++
    • Data Structures C++
    • C++ Programs
  • Typing Guide
  • Blogs
Search