Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

For a polynomial of order n with unknown coefficients, what are the ways to find the coefficients from n+1 points on its plot?

I remember one way is to construct a fractional for each point, and the polynomial is the sum of the fractionals, s.t. for each fractional, its value is the desired value for its corresponding point and zero for other points. Is there a name for the method?

Thanks!

share|improve this question
add comment

1 Answer 1

up vote 2 down vote accepted

The method you are talking about is called Lagrange Interpolation. If you want to find out the individual coefficients in the original "basis", then you would need to solve a $(n+1) \times (n+1)$ Linear system.

What we are essentially doing in Lagrange Interpolation is to shift to a new "basis" which depends on the points at which we observe the value, so that the system we need to solve is just the Identity matrix and hence we do not need to invert it as such to get the coefficients.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.