A type of inversion in which the error, \mathbf{e}, between observed and modeled data is minimized. This method can only be applied when there are more observations, \mathbf{d},  than unknown model parameters, \mathbf{m}. To obtain the unknown model parameters the matrix, Q, that relates the model parameters to the observations has to be inverted. Since this matrix is not square, the pseudo inverse of Q, Q^\dagger, is given by:

Q^\dagger = (Q^TQ)^{-1}Q^T

where Q^T is the transpose of Q and (Q^TQ) ^{-1} is the inverse of Q^TQ. The solution to the least squares problem would then be given by:

\mathbf{m} = Q^\dagger \mathbf{d}