ABSTRACT
In this chapter, the authors explore the numerical aspect of their work, illustrating with an array of examples the utility of the new approach to accelerating the convergence of Chebyshev series. Accelerating the convergence of Chebyshev expansions for function of interest, that is, making a change of variable which causes the coefficients in the series to go to zero faster than they would ordinarily, requires a new approach. The Chebyshev coefficients of a function with singularities “near” the interval decay more slowly than those of a function whose singularities are “far away” from the interval of representation. The authors develop an asymptotic representation for the Chebyshev coefficients associated with their functions of interest. They use the Clenshaw method to compute all of our Chebyshev coefficients, and illustrate the applicability of the method with several examples.
