Difference between revisions of "Lagrange Interpolation Formula"
ComplexZeta (talk | contribs) |
|||
Line 6: | Line 6: | ||
</center> | </center> | ||
− | + | While this formula may appear intimidating, it's actually not so difficult to see what is going on: for each term in the sum, we are finding a polynomial of degree <math>n</math> that goes through the points <math>(x_i,y_i)</math> and <math>(x_k,0)</math> for <math>k\neq i</math>. When we add them all together, we end up with a polynomial that interpolates the desired points. | |
{{stub}} | {{stub}} |
Revision as of 10:29, 19 February 2007
For any distinct reals and any reals , there exists a unique polynomial of degree less than or equal to such that for all integers , , and this polynomial is
.
While this formula may appear intimidating, it's actually not so difficult to see what is going on: for each term in the sum, we are finding a polynomial of degree that goes through the points and for . When we add them all together, we end up with a polynomial that interpolates the desired points.
This article is a stub. Help us out by expanding it.