Curve fitting with Chebyshev polynomials

A method is presented approximating a data set with additional conditions in an interval using Chebyshev polynomials. An appropriate segmentation of the interval allows in each interval a Chebyshev approximation of low degree and altogether less Chebyshev coefficients may be needed than in the case of a unique approximation of high degree for the whole interval. At the boundaries of the inner segments we demand continuity up to the second derivative as well as the fulfilment of given values at the border intervals. We use the least square method and introduce Lagrange factors to determine the Chebyshev coefficients. The result is a system of linear algebraic equations which has to be solved numerically.