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Table of Contents Bivariate Data Smoothing Curve Fitting by Splines | |
Assume that we have n+1 data points [x_{i}, y_{i}] with i=0 to n, and x_{0} < x_{1} < .... < x_{n}. Then the function S(x) is called a Cubic Spline if there exist n cubic polynomials s_{i}(x) having the coefficients a_{i,0}, a_{i,1}, a_{i,2}, a_{i,3} that satisfy the following conditions:
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Please note that there exists a unique cubic spline (called natural spline) with the boundary conditions S"(x_{0}) = 0 and S"(x_{n}) = 0. The natural spline is the curve obtained by forcing a flexible elastic rod through the points but letting the slope at the ends be free to equilibrate to the position that minimizes the oscillatory behavior of the curve.
Last Update: 2006-Jän-18