# Lagrange Interpolation Formula with Solved Example

## 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 **X**** _{1.5}** 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

## Solved Example

Lagrange’s Interpolation Solved Example

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

x | 5 | 7 | 11 | 13 | 17 |

y=f(x) | 150 | 392 | 1452 | 2366 | 5202 |

Now apply the lagrange formula to this table and solve.

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

X = 9 | X0 = 5 |

X1 = 7 | X2 =11 |

X3 = 13 | X4 = 17 |

Also, value of function **f( xi )**.

f(x0) =150 | f(x1)=392 |

f(x2) =1452 | f(x3) =2366 |

f(x2) =5202 |

Now, Simplify the polynomial

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

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