Algorithm 227: Chebyshev polynomial coefficients

Let XlC${X_{l}^{C}}$ be the set of l Chebyshev points in the interval [ 1,1]. If n and n0 are such that n=2mn0 1 for some positive integer m, then Xn0C XnC$X_{n_{0}}^{C} \subset {X_{n}^{C}}$. This property can be utilized in order to reuse previous ...

When a function is singular at the ends of its expansion interval, its Chebyshev coefficients a"n converge very poorly. We analyze three numerical strategies for coping with such singularities of the form (1+/-x)^klog(1+/-x), and in the process make ...

Laurent Padé-Chebyshev rational approximants,A_m(z,z⁻¹)/B_n(z, z⁻¹), whose Laurent series expansions match that of a given functionf(z,z⁻¹) up to as high a degree inz, z⁻¹ as possible, were introduced for first kind Chebyshev polynomials by Clenshaw ...