On the uniform convergence of a collocation method for a class of singular integral equations

We establish the uniform convergence of a collocation method for solving a class of singular integral equations. This method uses the Jacobi polynomials {P_n^{(, )}} as basis elements and the zeros of a Chebyshev polynomial of the first kind as collocation points. Uniform convergence is shown to hold under the weak assumption that the kernel and the right-hand side are Hölder-continous functions. Convergence rates are also given.