Two dimensional data modeling and Chebyshev approximation of spline

This paper describes the approximation of discrete data using splines. The approximation method is adapted from the Chebyshev approximation. The procedures to find a set of extreme points for incoming discrete data are proposed. Several algorithms using cubic spline and Lagrange polynomial are proposed to diffrentiate the results due to the number of iteration, total number of the set of extreme points and error generated. The results show that the error generated decreases as the total number of extreme points increase. Six extreme points can represent one hundred of points and the generated error can be decreased. However, the algorithm presented uses more number of extreme points and will cause an increase in the total number of iterations