Accurate evaluation of a polynomial in Chebyshev form

This paper presents a compensated algorithm to accurately evaluate a polynomial expressed in Chebyshev basis of the first and second kind with floating-point coefficients. The principle is to apply error-free transformations to improve the traditional Clenshaw algorithm. The new algorithm is as accurate as the Clenshaw algorithm performed in twice the working precision. Forward error analysis and numerical experiments illustrate the accuracy and properties of the proposed algorithm.