Color matching today is based upon the metamerism principle which necessitates agreement of only a trichromatic specification. The amounts of a set of three dyes (e.g., cyan, magenta, and yellow) to reach a certain chromaticity and lightness (u,v,Y) is decided uniquely when the spectral density distributions of the dyes are known. The problem of calculating the amount of dye is reduced to solving simultaneous integral equations, which is not always easy. The calculation was executed conventionally by changing the dye amount systematically and selecting the combination of dye amount that gave the least color difference. This systematic sweeping method is not efficient, so that it takes more than 10 min to calculate a set of dye amount within 0.001 C.I.E. (1964) color difference, even with a computer. The author investigated the computer program of fast color matching for routine work by means of matrix representation between dye amount and trichromatic specification.
N. Ohta, "Fast Computing of Color Matching by Means of Matrix Representation. Part 1: Transmission-Type Colorant," Appl. Opt. 10, 2183-2187 (1971)