The Lanczos method applied to quasi-static stark broadening of spectral lines

The quasi-static ion approximation of Stark broadened spectral lines involves an average of the field-dependent line shape over the microfield probability distribution. In the conventional approach, this can become computationally expensive since the calculation at each field point requires inverting a possibly large matrix. It is shown that these calculations are well suited to the “Padé Via Lanczos” approach, which allows for an efficient and accurate numerical integration over the quasi-static field. In turn, the integration forms the basis for determining convergence with Lanczos iterations. Simple examples are used to demonstrate improved performance over conventional methods.