If we are given the spectrophotometric curves of a color and three colorants to be used in matching it, the computation of the concentrations of the three colorants required for a tristimulus match is a complicated nonlinear problem. However, with the help of an approximating assumption, a linear solution may be obtained by a matrix inversion technique. Although this is an approximate solution, it is better the less metameric the match. With this rough solution as a starting point, iteration may be used to approach an exact match to any desired degree of accuracy. The inverted matrix used for the iterative computation is identical to that used for the rough solution.
EUGENE ALLEN, "Basic Equations Used in Computer Color Matching," J. Opt. Soc. Am. 56, 1256-1257 (1966)