Illustration of the MATISSE basis functions. For every set of parameters θ_i, corresponding to a spectrum in a grid of synthetic spectra, a set of B_θ(λ) was computed. Here, we can see the computed B_Teff(λ) functions (and the corresponding synthetic spectrum) for a star with T_eff = 5250 K, log    g = 4.5, [M/H] = −0.75 dex, [α/Fe] = 0.3 dex. For clarity we represent only a part of the wavelength range in the plot. The strongest features in the spectrum (top panel), identified with dashed vertical lines, correspond to the Ca ii triplet. In the second row we show the B_Teff(λ) computed with a direct inversion of the correlation matrix, whereas the last two panels show the B_Teff(λ) functions computed with the Landweber iterative algorithm, imposing a coefficient of correlation between the input and the output parameters of 0.97 and 0.80, respectively. As described in Sect. 2.1, the smaller the coefficient, the less weight is given to the second-order variations of the spectral flux. The spectral analysis can therefore be optimised according to the quality of the spectrum, which is typically quantified in the signal-to-noise ratio.