## Interpolator

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Interpolator

*
See also* -
Lagrange interpolation

**What is the**

The

*Interpolator*?*Interpolator*, as I have called it, is a program written in Mircosoft Excel which, given up to 8 (x,y) coordinate pairs, will estimate values for y for a given x within the range of the coordinate pairs. This is done by finding a polynomial line that goes through all the coordinate pairs.

interpolator.xls | |

File Size: | 79 kb |

File Type: | xls |

(Version 1.10, 78.0 KB)

Below is a screenshot from the program...

**What does the**

You enter up to eight (x,y) co-ordinate pairs. The interpolator then...*Interpolator*do?- gives the equation of the curve that passes through all these points,
- calculates a corresponding value of y for a given x within the range of the coordinate pairs,
- draws the curve on a graph, along with the (x,y) coordinate pairs.

Below is a screenshot from the program...

**How does the**

*Interpolator*work?The program uses Lagrange's interpolation forumla. This formula takes the (x,y) coordinate pairs and uses them to calculate the coefficients of the terms of the (unique) polynomial curve. If you want to find out more, I'd suggest reading my page on Lagrange interpolation.

**Where did you get the information to write the**

I first came across Lagrange's interpolation formula in Jean Meeus' book

*Interpolator*?*Astronomical Algorithms*, but the formula is widely known and easily found online (for example, see mathworld).