In colorimetric work, the calculation of tristimulus values is typically accomplished by one of the standard numerical-integration schemes, such as Simpson’s rule. However, great computational savings can be achieved by use of a more-sophisticated approach. By computing the orthogonal polynomials associated with the CIE color-matching functions, the method of gaussian quadratures can be applied. For certain types of color-matching problems, the gaussian technique is at least twice as fast, for the same accuracy, as conventional methods.
Robert Wallis, "Fast computation of tristimulus values by use of gaussian quadrature," J. Opt. Soc. Am. 65, 91-94 (1975)