A DOMAIN DECOMPOSITION METHOD FOR GENERATING ORTHOGONAL POLYNOMIALS FOR A GAUSSIAN WEIGHT ON A FINITE INTERVAL

A domain decomposition method has been developed for generating orthogonal polynomials for a Gaussian weight on (-1, 1). The method takes advantage of the underlying asymptotic structure of the orthogonal polynomials and, hence, it is effective in the sense that it makes maximal use of the analytic properties of the solution to increase accuracy and efficiency. These polynomials are necessary for constructing Gaussian quadrature formulas that are encountered in large quantum chemistry computational packages and in calculating the Compton scattering kernel and its associated angular moments. © 1992.