Corrigendum

Abstract

A New Method for Multivariate Calibration

Ralf Marbach

VTT Electronics, Kaitoväylä 1, 90571 Oulu, Finland. E-mail: [e-mail]

Two equations in this paper [R. Marbach, J. Near Infrared Spectrosc. 13(5), 241–254 (2005)] were printed wrongly. The online version is now correct, and the correct equations are reproduced below.

${\mathbf{b}}_{\mathit{\text{eq}}}=\frac{[\mathbf{I}-\mathbf{K}{({\mathbf{K}}^T\mathbf{K})}^{-1}{\mathbf{K}}^T]\cdot \mathbf{g}}{{\mathbf{g}}^T\cdot [\mathbf{I}-\mathbf{K}{({\mathbf{K}}^T\mathbf{K})}^{-1}{\mathbf{K}}^T]\cdot \mathbf{g}}$ (13)

$\begin{array}{c}\mathbf{b}=\frac{{(\Sigma +{\sigma }_{chol,u}^2{\mathbf{g}}_{chol}{\mathbf{g}}_{chol}^T+{\sigma }_{chol,u}^2{s}^2{r}^2{\mathbf{g}}_{tri\mathbf{g}}{\mathbf{g}}_{tri\mathbf{g}}^T)}^{-}{\mathbf{g}}_{chol}}{{\mathbf{g}}_{chol}^T{\left(\Sigma +{\sigma }_{chol,u}^2{\mathbf{g}}_{chol}{\mathbf{g}}_{chol}^T+{\sigma }_{chol,u}^2{S}^2{r}^2{\mathbf{g}}_{tri\mathbf{g}}{\mathbf{g}}_{tri\mathbf{g}}^T\right)}^{-}{\mathbf{g}}_{chol}}\\ =\frac{{\left(\Sigma +{\sigma }_{chol,u}^2{S}^2{r}^2{\mathbf{g}}_{tri\mathbf{g}}{\mathbf{g}}_{tri\mathbf{g}}^T\right)}^{-}{\mathbf{g}}_{chol}}{{\mathbf{g}}_{chol}^T{\left(\Sigma +{\sigma }_{chol,u}^2{S}^2{r}^2{\mathbf{g}}_{tri\mathbf{g}}{\mathbf{g}}_{tri\mathbf{g}}^T\right)}^{-}{\mathbf{g}}_{chol}}\end{array}$ (25)