Complex polynomial approximation by the Lanczos τ-method: Dawson's integral

摘要

The Lanczos τ-method, with perturbations proportional to Faber polynomials, is used to obtain polynomial approximations for Dawson's integral on circular sectors. An upper bound on the truncation error is established for one form of the τ-method, which gives near-minimax polynomial approximations, and it is found that this bound provides a useful estimate of the truncation error. The Faber series for Dawson's integral on a circular sector is also investigated. Numerical results show that the τ-method can produce polynomial approximations as accurate as the truncated Faber series, with much less effort than is involved in computing the Faber coefficients.