Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Bivariate Data Curve Fitting Curve Fitting by Splines  
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:
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.


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Last Update: 20121008