When the number of primary colors, N, is greater than three, the solutions that present the same XYZ values have N – 3 dimensional freedom. A multiprimary display expands the color gamut and also produces many sets of display signals that present a given set of XYZ tristimulus values, so it can utilize the degrees of freedom. The spectral approximation method is thus well suited for multiprimary displays. It minimizes the difference between the original spectrum and the reproduced spectrum under the constraint of a tristimulus match for a CIE standard observer, so it should reduce the color mismatch for any color matching function. However, this had not been confirmed using actual images. The spectral approximation method may not work well for actual images because such images usually have many colors and shadings, and interactions among them might reduce its effectiveness. Since multiprimary displays are becoming commonly used for electronic commerce, telemedicine, etc., confirming the effectiveness of this method is important. Therefore we conducted a visual experiment using actual images to determine its performance. Comparison with other decomposition methods that do not use spectral approximation suggests the effectiveness of the spectral approximation method. We also developed an algorithm for the spectral approximation method that algebraically derives an optimal solution and yields more precise results with less computational cost than Murakami's one.