**Interpolation** - it's just finding middleware, unknown value (numbers) Y_{1} at a known number of X_{1} within the limits certain boundaries (X_{0}...X_{n}) && (Y_{0}...Y_{n}), where each X value is associated with the value ofУ.

It is not clear that such interpolation? Let me explain simply an example:

Imagine that you need to run a distance of 10 (km) (10 → 0)! Here you come to the starting line and start to run the race! Immediately from the start you ran at a speed 18 (km/hr). That you run, run and your speed gradually and evenly falls in overcoming distance. You run up to the finish line 0 (km) and cross it at a speed of already 3 (km/hr).

And you began to wonder what was your speed by 5 (km) from the finish? Can all known data presented in the form table below:

km | km/hr |
---|---|

x_{0} = 10 | y_{0} = 18 |

x_{1} = 5 | y_{1} = ? |

x_{n} = 0 | y_{n} = 3 |