Lagrange Interpolation: Equal Spacing
- Ryan Hirst
Showing the simplifications that can be made if the points are evenly spaced.
If we write the order n-1 polynomial as the system , where [list]
M is the nxn matrix of the abscissae (x-values of the tabular points),
x is the vector of unknown coefficients
y the y-values at the given abscissae
Then the Coefficients x are given by
If the points are equally spaced, for a given order n, the matrix M is constant. It can be calculated once, and used for all curves of the same order. By choosing n odd, and taking the midpoint of the interval as the zero point, the matrix can be further simplified.