Interpolation is defined as the technique of calculating the value of a function for any intermediate value of independent variable. If we are given the various values of y=f(x) for a given set of value of x, then the process of finding the value of y corresponding to any value of x is called as an interpolation.

The value of y can be found for the given range of x0 to xn or inside the given range is called interpolation.

While the process of computing the value of function outside the given range is called extrapolation.

### Engineering Applications:

Yes, you heard right. Interpolation is required in Engineering and scientific investigation.

e.g.

For a particular case, the various values of the current and voltage are measured and tabulated below as

I(Amp) | 0.8 | -0.65 | 0.92 | 1.23 |

V(Volts) | 0.32 | 0.89 | 1.03 | 2.12 |

Then the voltage drop across the current I=0.9 Amp. can be calculated by interpolation.

In this post we will see the various methods of interpolation. They are,

- Lagrange's interpolation
- Newton's Forward Difference Interpolation
- Newton's Backward Difference Interpolation
- Hermite Interpolation

Hermite Interpolation

Newton Forward Interpolation

Newton Backward Interpolation

Langint interpolation